welcome to math with Mr Jay [Music] this video I'm going to go through a complete guide to greatest common factor and least common multiple I will cover everything from the basics to different strategies to working with three numbers we will start with the greatest common factor and specifically an intro where we will take a look at factors common factors and greatest common factor so we will cover the basics in this section then we will move on to two more examples followed by taking a look at a different strategy we can use to find the greatest common factor and then we will end with finding the greatest common factor of three numbers after that we will take a look at least common multiple now when we think of factors of a number we need to think what numbers can we multiply to equal that given number or what numbers can we divide that given a number by evenly so divide with no remainder now it's not the most technical or mathematical way to word it but you can think what numbers go into the given number this will all make a lot more sense as we go through our example let's jump into our example where we have 12 and 18. we're going to list the factors of 12 and 18 then find common factors and then lastly find the greatest common factor which is also referred to as the GCF let's start with the factors of 12 and my suggestion would be to always start with one and the number itself we can think of factors in terms of pairs so 1 times 12 equals 12 or we can divide 12 by those factors however you want to to think about it so I'm going to write 1 and 12 with a gap in between that way we can write the other factors in between 1 and 12 and we can write them in order now we need to list the other factors of 12. so let's think about what else goes into 12 so to speak think of multiplication facts division facts and we can work our way up from one so there are different strategies and ways to work through this the next factors are two and six two times six equals 12. so 2 and 6 are factors of 12. so two and six then we have three and four three times four equals twelve so three and four are factors of 12 as well and again we can also think of these factors in terms of division we can divide 12 evenly by these factors now are there any more factors of 12 no we are done that's our list of factors for 12. let's move on to the factors of 18. we will start with 1 and 18. so 1 and 18 with the Gap in between next we have two and nine two times nine equals eighteen so two and nine are factors then we have three and six three times six equals eighteen so three and six are factors of 18. and that's it for the factors of 18. you can always try more if you're unsure if you have all of the factors for example we can think about four five seven eight and so on but we are done that's our list of factors for 18. one thing I do want to mention about factors and writing out these Factor lists is that you will get better the more you do so writing the factors the spacing of your lists or whatever else the case may be so something to keep in mind now let's take a look at the common factors between 12 and 18. that just means the factors they share the factors they have in common so one is a common factor two is a common factor three is a common factor and then six is a common factor so the common factors between 12 and 18 are one two three and six now we have the greatest common factor or GCF that's just the greatest factor in value that they share or have in common the greatest common factor between 12 and 18 is 6. so the greatest common factor equals six so there is an intro to factors common factors and greatest common factor let's move on to two more examples here are our next two examples and we will find the greatest common factor just like we did in the intro by listing the factors of the given numbers so again the greatest common factor is going to be the greatest or largest factor in value that both numbers share that both numbers have in common let's jump into our examples and see exactly what this looks like starting with number one where we have 16 and 24. we first need to list the factors of each number let's start with the factors of 16. now I would suggest always starting with the factors of 1 and the number itself because we know one times that number will equal that number itself we can think of factors in terms of pairs 1 times 16 equals 16 or we can think of it in terms of division we can divide 16 by those factors evenly however you want to think about it so I'm going to write 1 and 16 with a gap in between for the other factors that way we can write the factors in order now we need to list the other factors of 16. so let's think about what else goes into 16 so to speak think about multiplication facts division facts and we can work our way up from one so there are different strategies and ways to work through this the next factors of 16 are 2 and eight two times eight equals sixteen so two and eight are factors of 16. and then our last factor of 16 is four four times four equals sixteen so four is a factor of 16. although four times four equals sixteen we only need to write four Once in our factors list and that's it for the factors of 16. you can always think about other possible factors if you're unsure if you're done for example three five six and so on but we have them all the factors of 16 are one two four eight and sixteen let's move on to the factors of 24. we will start with 1 and 24. next we have two and twelve two times twelve equals 24. so 2 and 12 are factors of 24. then we have 3 and 8 3 times 8 equals 24 so 3 and 8 are factors of 24 and then lastly we have four and six four times six equals 24 so 4 and 6 are factors of 24. and that's it for the factors of 24. one two three four six eight twelve and twenty four now that we have the factors listed for our numbers we need to look for common factors and specifically the greatest common factor so let's look for factors that these numbers share that they have in common so one is a common factor two is a common factor four is a common factor and then eight is a common factor so the greatest common factor is eight the greatest factor in value that they share the greatest factor in value that they have in common so the GCF the greatest common factor is eight the greatest common factor of 16 and 24 is eight let's move on to number two where we have 15 and 35. let's start with the factors of 15. we have 1 and 15. next we have three and five three times five equals fifteen so three and five are factors of 15. and that's it for the factors of fifteen one three five and fifteen now let's list the factors of 35 so we have one and 35 and then 5 and 7 5 times 7 equals 35 so 5 and 7 are factors of 35 and that's it for the factors of 35 1 5 7 and 35. now that we have our factors list for our numbers we need to look for common factors and specifically the greatest common factor so 1 is a common factor and then 5 is a common factor that means 5 is the greatest common factor so the GCF the greatest common factor is five the greatest common factor of 15 and 35 is 5. so there are two examples of finding the greatest common factor by listing the factors of the numbers let's move on to finding the greatest common factor using prime factorization here are our examples for finding the greatest common factor by using prime factorization now I like using this strategy and find it helpful when working with numbers that are a little larger in value and not as simple to work with for example the strategy of listing out all of the factors of the numbers in order to find the GCF can be kind of difficult and time consuming when working with larger numbers in value so this is a different approach a different strategy to be familiar with when it comes to finding the greatest common factor let's jump into our examples starting with number one where we have 63 and 84. let's start with the prime factorization of 63 and we will start with the factors of 7. and nine seven times nine equals 63 so 7 and 9 are factors of 63. now 7 is prime so we are done there 9 we can break down three times three equals nine so three is a factor of nine three is prime so we are done there and there and that's the prime factorization of 63. we can't break that down any further now we have the prime factorization of 84. let's start with the factors of 2 and 42 2 times 42 equals 84. so 2 and 42 are factors of 84. now 2 is prime so we are done there 42 we can break down 2 times 21 equals 42. so 2 and 21 are factors of 42. 2 is prime so we are done there 21 we can break down three times seven equals 21. so 3 and 7 are factors of 21. 3 is prime and 7 is prime as well so we are done that's the prime factorization of 84. we can't break that down any further now that we have the prime factorization of both of those numbers we need to find common prime factors so prime factors that they share now I'm going to list the prime factors of each to make it easier to find the ones they have in common so as far as 63 we have three three and seven three times three times seven equals 63. 484 we have two two three and seven two times two times three times seven equals Eighty-Four now we need to find any common prime factors three is a common prime factor and 7 is a common prime factor so they have a 3 and a 7 in common once we find those common prime factors we multiply them so three times seven and that equals 21 and that's our greatest common factor so the GCF the greatest common factor of 63 and 84 is 21. let's move on to number two where we have 48 and 72. let's start with the prime factorization of 48 and we will start with the factors of 2 and 24. 2 times 24 equals 48 so they are factors now 2 is prime so we are done there we can break down 24. 2 times 12 equals 24 so 2 and 12 are factors 2 is prime so we are done there we can break 12 down further 2 times 6 equals 12 so 2 and 6 are factors 2 is prime so we are done there but we can break 6 down further two times three equals six so two and three are factors 2 is prime so we are done there and 3 is prime so we are done there as well and we are done with the prime factorization of 48. we can't break that down any further now we need the prime factorization of 72. let's start with the factors of 2 and 36 2 times 36 equals 72 so they are factors 2 is prime so we are done here 36 we can break down 2 times 18 equals 36 so 2 and 18 are factors 2 is prime so we are done there 18 we can break down two times nine equals 18 so 2 and 9 are factors 2 is prime so we are done there but we can break nine down further three times three equals nine so three is a factor of nine three is prime so we are done there and there and we are done with the prime factorization of seventy-two we can't break that down any further now that we have the prime factorization of both 48 and 72 we need to find common prime factors so I'm going to write the prime factors of 48 and 72 that way it's a little easier to find common prime factors for 48 we have two and three so two times two times two times two times three equals 48 472 we have two two two three and three two times two times two times three times three equals 72. now we need to find common prime factors they have a 2 in common another two in common another two in common and then a three in common so now that we found the common prime factors we need to multiply them to get the greatest common factor so we have two times 2 times 2 they have three twos in common times three two times two is four times two is eight times three is twenty-four so the GCF the greatest common factor of 48 and 72 is 24. so there's how to find the greatest common factor using prime factorization let's move on to finding the greatest common factor of three numbers here is our example for finding the greatest common factor of three numbers and in this example we will use the strategy of listing out the factors of the numbers let's jump into our example where we have 27 9 and 18. we will start by listing the factors of each and then find the greatest common factor let's start with the factors of 27 now I would suggest always starting with the factors of 1 and the number itself because we know one times that number will equal that number itself we can think of factors in terms of pairs 1 times 27 equals 27 or we can divide 27 by those factors evenly however you want to think about it so I'm going to write 1 and 27 with a gap in between for the other factors that way we can write the factors in order now we need to list the other factors of 27 so let's think about what else goes into 27 so to speak think about multiplication facts division facts and we can work our way up from one so there are different strategies and ways to to work through this the next factors of 27 are 3 and 9. 3 times 9 equals 27 so 3 and 9 are factors of 27 and that's actually it for the factors of 27. you can always think about other possible factors if you're unsure if you're done for example 2 4 5 6 and so on but we have them all 1 3 9 and 27 and like I mentioned earlier we can also think of these factors in terms of division we can divide 27 evenly by all of these factors now one thing I do want to mention about factors and writing out factors lists is that you will get a lot better the more you do everything from writing and recognizing factors to the spacing of your lists so something to keep in mind let's move on to the factors of 9 and we can start with one and nine now we need to think of other factors of nine well three times three equals nine so three is a factor of nine and although three times three equals nine we just need to put three once there as far as the list of factors lastly let's list the factors of 18. we can start with one and 18. next we have two and nine two times nine equals eighteen so two and nine are factors of 18. and then lastly we have three and six three times six equals eighteen so three and six are factors of eighteen and that's it for the factors of eighteen one two three six nine and eighteen now that we have all of the factors listed for our numbers we need to look for common factors so factors they share and then specifically we need to look for the greatest common factor so the greatest factor in value that they all share that they all have in common so one is going to be a common factor three is going to be a common factor and then 9 is going to be a common factor so there are three common factors between these numbers now the greatest common factor is going to be nine so over to the right I'll write the GCF which stands for the greatest common factor equals 9. so the greatest common factor of these three numbers 27 9 and 18 is 9. so there's how to find the greatest common factor of three numbers by listing the factors of the numbers let's move on to another example where we will use prime factorization here is our example for finding the greatest common factor of three numbers using prime factorization let's jump into our example where we have 54 36 and 90. so we need to find the greatest common factor of those three numbers let's start with the prime factorization of all three of our numbers starting with the prime factorization of 54. 2. times 27 equals 54. so 2 and 27 are factors of 54. now 2 is prime so we are done there 27 we can break down three times nine equals 27. so 3 and 9 are factors of 27. 3 is prime so we are done there 9 we can break down three times three equals nine so three is a factor of nine three is prime so we are done there and there and that's the prime factorization of 54. we can't break that down any further let's move on to the prime factorization of 36. 2 times 18 equals 36 so 2 and 18 are factors 2 is prime so we are done there we can break 18 down further two times nine equals eighteen so two and nine are factors 2 is prime so we are done there we can break nine down further three times three equals nine so three is a factor of nine three is prime so we are done there and there and that's the prime factorization of 36. we can't break that down any further and then lastly we have the prime factorization of ninety 2 times 45 equals 90. so 2 and 45 are factors 2 is prime so we are done there 45 we can break down further five times nine equals 45 so 5 and 9 are factors 5 is prime so we are done there 9 we can break down three times three equals nine so three is a factor 3 is prime so we are done there and there and that's the prime factorization of 90. we can't break that down any further now that we have the prime factorization of all three of our numbers we need to look for common prime factors so prime factors that all three of our numbers share that they all have in common now in order to make it easier to find common prime factors I'm going to list the prime factors off to the side here starting with 54. so we have 2 foreign three and three two times three times three times three equals fifty-four now let's move on to 36 we have two two three and three two times two times three times three equals thirty-six and then lastly we have 90. 2 3 3 and 5. 2 times 3 times 3 times 5 equals ninety now that we have the prime factors listed we need to look for common prime factors so factors that all three of these numbers share so two is a common prime factor three is a common prime factor and then we have another three in common the common prime factors are two three and three now once we have those common prime factors we multiply them to get the greatest common factor two times three is six times three is eighteen so the GCF the greatest common factor of 54 36 and 90. all right is 18. so there's how to find the greatest common factor of three numbers using prime factorization and that's a wrap for the greatest common factor portion of this video let's move on to least common multiple let's start the least common multiple portion of this video with an intro we will take a look at multiples common multiples and least common multiples so we will cover the basics in this section then we will move on to two more examples followed by taking a look at a different strategy we can use to find the least common multiple and then we will end with finding the least common multiple of three numbers now a multiple is the result of multiplying a given number by an integer so when we think of the multiples of a number we need to think about the numbers we get when multiplying that given number by integers a simpler way to think about multiples is to think about skip counting so all of the numbers something is going to hit when you count up by that number those are all going to be multiples this will make a lot more sense as we go through our example let's jump into our example where we have 6 and 15. we're going to list some multiples of 6 and 15. look at common multiples and then find the least common multiple also referred to as the LCM let's start with the first five multiples of six which are six times one which is six six times two is twelve six times three is eighteen six times four is twenty four and six times five is thirty so those are the first five multiples of six and you can see that we just skip counted by six six twelve eighteen twenty four Thirty so on and so forth now I stopped at 30 because multiples go on forever they are endless they are infinite my suggestion is to list four or five multiples when looking for common multiples or the least common multiple so list four or five look for any in common and if you don't have any in common you can always extend the multiples lists now let's list the first five multiples of fifteen so fifteen times one is fifteen 15 times 2 is 30 15 times 3 is 45 15 times 4 is 60 and then 15 times 5 is 75. now let's look for any common multiples so any multiples they share any multiples they have in common well 30 is a common multiple the next common multiple is 60. so let's extend the list of multiples for 6 there to show another common multiple so after 30 we have 36 then 42 then 48 then 54. then 60. so another common multiple is 60. but again remember multiples lists go on forever so we have an infinite amount of common multiples so down below for common multiples I'll put 30 60 and then make note that we have an infinite amount of common multiples now we have the least common multiple which is just the smallest number in value that they have in common the smallest number and value that they share this is going to be 30. the least common multiple or LCM between 6 and 15 is 30. so there's an intro to multiples common multiples and least common multiple let's move on to two more examples here are our next two examples and we will find the least common multiple just like we did in the intro by listing multiples of the given numbers now as far as the least common multiple between numbers this is going to be the smallest multiple in value that both numbers share this will make a lot more sense as we go through our examples let's jump into our examples starting with number one where we have 9 and 12. we're going to start by listing some multiples of both 9 and 12. then we will look for common multiples and specifically the least common multiple also referred to as the LCM let's start with some multiples of nine which are nine times one which is nine nine times two is eighteen nine times three is twenty 7 9 times 4 is 36 and 9 times 5 is 45 so you can see that we just skip counted by 9 to list those multiples 9 18 27 36 45 so on and so forth now I stopped at 45 because multiples go on forever they are endless they are infinite my suggestion is to list four or five multiples when looking for the least common multiple so list four or five multiples for each number look for any in common and if you don't have any in common you can always extend the multiples lists now let's list the first five multiples of twelve twelve times one is twelve twelve times two is twenty four twelve times three is thirty-six twelve times four is forty eight and twelve times five is sixty so again you can see that we skip counted there we skip counted by twelve so 12 24 36 48 60 so on and so forth now that we have some multiples listed for both 9 and 12 we need to look for any common multiples so any multiples that they share and then specifically we need to look for the least common multiple well 36 is a common multiple and it's going to be the least common multiple so the smallest multiple in value that they share so let's write that the LCM which stands for least common multiple is 36. so the least common multiple of 9 and 12 is 36. now one thing I do want to mention about common multiples is that they are infinite although we only have one common multiple in our lists as is 36 we can always extend multiples lists so we can always keep going to find more common multiples remember multiples are endless so that means common multiples are endless so that's just something to think about when it comes to multiples let's move on to number two where we have 10 and 25. let's start with some multiples of 10. so 10 times 1 is 10 10 times 2 is 20 10 times 3 is 30 10 times 4 is 40. and then 10 times 5 is 50. so 10 20 30 40 50 so on and so forth now let's list the first five multiples of 25 so 25 times 1 is 25 25 times 2 is 50 25 times 3 is 75 25 times 4 is 100 and then 25 times 5 is 125. now that we have some multiples listed we can look for common multiples and specifically the least common multiple well 50 is a common multiple and it happens to be the least common multiple so the LCM is 50 the least common multiple of 10 and 25 is 50. so there are two examples of finding the least common multiple by listing some multiples of the given numbers let's move on to finding the least common multiple using prime factorization here are our examples for finding the least common multiple by using prime factorization now I like using this strategy and find it helpful when working with numbers that are a little larger in value and not as simple to work with for example the strategy of listing out multiples of numbers in order to find the LCM can be kind of difficult and time consuming when working with larger numbers in value so this is a different approach a different strategy to be familiar with when it comes to finding the least common multiple let's jump into our examples starting with number one where we have 15 and 27. let's start with the prime factorization of 15 and we will start with the factors of 3 and five now three is prime so we are done there and 5 is prime so we are done there as well and that's the prime factorization of 15. we can't break that down any further now we have the prime factorization of 27. let's start with the factors of 3 and 9. 3 times 9 equals twenty-seven so 3 and 9 are factors of 27. 3 is prime so we are done there but we can break 9 down 3 times 3 equals nine so three is a factor of nine three is prime so we are done there and there and that's the prime factorization of 27. we can't break that down any further now we're ready to move to the next step so we need to list the prime factors of 15 and 27 and match them vertically let's see what this looks like starting with 15. so our prime factors from the prime factorization are three and five or three times five now four 27 so we have three times three times three and you'll notice that big gap underneath the 5 there we are matching numbers vertically 27 does not have a prime factor of five so I left that blank underneath the 5. now that we have our prime factors listed and matched vertically we move on to the next step where we bring down and I like to draw a line underneath here in order to separate these steps so this is a column and although we have two threes here this is a column of Threes so we just bring one down we have a three to represent that column of two threes times we have a column of five here times we have a three here times another three here so we end up with three times five times three times three and by multiplying these we get our least common multiple so three times five is fifteen times three is forty-five times three is one hundred thirty-five and that's our least common multiple so the LCM the least common multiple of 15 and 27 is 135. let's move on to number two where we have 28 and 52. let's start with the prime factorization of 28. now 2 times 14 equals 28 so let's start with those factors 2 is prime so we are done there 14 we can break down two times seven equals 14. so 2 and 7 are factors of 14. 2 is prime so we are done there and 7 is prime as well so we are done there and that's the prime factorization of 28. we can't break that down any further now we need the prime factorization of 52. let's start with the factors of 2 and 26 2 times 26 equals 52. so 2 and 26 are factors of 52. 2 is prime so we are done there 26 we can break that down 2 times 13 equals 26. so 2 and 13 are factors of 26. 2 is prime so we are done there and 13 is prime as well so we are done there and that's the prime factorization of 52. we can't break that down any further now we need to list the prime factors and match them vertically for 28 we have two times two times seven 452 we have two times two times 13. now we need to bring down so we have a column of twos here so let's bring down a 2 to represent that column times another column of twos so let's bring another two down times 7 times 13. so we have 2 times 2 times 7 times 13 to get our least common multiple we have 2 times 2 which is 4 times 7 is 28 times 13. well I'm not sure what 28 times 13 is so let's come to the side here foreign 28 times 13. we will start with 3 times 8 which is 24 3 times 2 is 6 Plus 2. is 8. we are done here and done here we need a zero now we have one times eight which is eight and then one times two is two let's add four plus zero is four eight plus eight is 16 and then one plus two is three so we get 364. so the least common multiple of 28 and 52. let me squeeze this in here is 300 60 4 so there's how to find the least common multiple using prime factorization let's move on to finding the least common multiple of three numbers here is our example for finding the least common multiple of three numbers and in this example we will use the strategy of listing out some multiples of the given numbers let's jump into our example where we have 5 8 and 20. so let's find the least common multiple between these three numbers let's start with some multiples of five so five times one is five five times two is ten five times three is fifteen five times four is twenty and five times five is twenty-five so you can see that we just skip counted by five to list those multiples of five five ten fifteen twenty twenty five so on and so forth now I stopped at 25 because multiples go on forever they are endless they are infinite my suggestion is to list four or five multiples of each number when looking for the least common multiple so list four or five for each number look for any in common specifically the least common multiple and if you don't have any in common you can always extend the multiples lists now let's list the first five multiples of eight eight times one is eight eight times two is sixteen eight times three is twenty-four eight times four is thirty-two and then eight times five is forty so eight sixteen twenty four thirty two forty so on and so forth and then lastly let's list the first five multiples of 20 so 20 times 1 is 20. 20 times 2 is 40. 20 times 3 is 60 20 times 4 is 80. and then 20 times 5 is 100 so 20 40 60 80 100 so on and so forth now that we have some multiples listed for each number we can look for common multiples and specifically the least common multiple so the smallest multiple in value that they all share but as of right now we do not have any multiples that all three of these numbers share so we need to continue our lists now as far as our lists of multiples for the multiples of 20 we are at 100 for the multiples of eight we are at forty for the multiples of five we're only at 25 so let's extend the list of multiples of five so after 25 we have 30 then 35 and then 40. now 40 is going to be a common multiple a multiple that all of our numbers share and specifically it's going to be the least common multiple so again 40 is going to be our least common multiple so the LCM which stands for least common multiple is 40. so there's how we find the least common multiple of three numbers by listing out some multiples of the given numbers let's move on to another example where we will use prime factorization here is our example for how to find the least common multiple of three numbers using prime factorization let's jump into our example where we have 21 28 and 32. so we need to find the least common multiple of those three numbers let's start with the prime factorization of all three of our numbers starting with 21. three times seven equals 21 so 3 and 7 are factors of 21. now 3 is prime so we are done there 7 is prime as well so we are done there and that's the prime factorization of 21 we can't break that down any further let's move on to 28. 2 times 14 equals 28 so 2 and 14 are factors of 28. 2 is prime so we are done there 14 we can break down two times seven equals 14. so 2 and 7 are factors of 14. 2 is prime so we are done there 7 is prime as well so we are done there and that's the prime factorization of 28. we can't break that down any further lastly we have the prime factorization of 32. 2 times 16 equals 32 so 2 and 16 are factors of 32. 2 is prime so we are done there 16 we can break down two times eight equals 16. so 2 and 8 are factors of 16. 2 is prime so we are done there we can break eight down further two times four equals eight so two and four are factors of eight two is prime so we are done there we can break four down further 2 times 2 equals 4 so 2 is a factor of 4. 2 is prime so we are done there and there and that's the prime factorization of 32. we can't break that down any further now that we have the prime factorization of all three of our numbers we need to list the prime factors and match them vertically let's start with the prime factors of 21. so 3 and seven three times seven equals 21. now for the prime factors of 28 and I'm going to start with the prime factor of 7 since 21 also has a prime factor of seven I'm matching the sevens vertically then we have 2 and 2. so 7 times 2 times 2 equals 28 and then lastly we have the prime factors of 32. we have a 2 that we can match vertically another two that we can match vertically and then three more twos now that we have our prime factors listed and matched vertically we need to bring down a number to represent each column and it's going to be one for each column you'll see what this means as we go through this step so I like to draw a line to separate our steps here and now again we need to go through each column and bring down a number to represent that column for example we have a three column right here even though there's one three that's okay we have a three column there so let's bring down a three to represent that column times we have a seven column here now there are two sevens there but we only bring down one seven to represent that column times next we have a column of twos so bring down a two to represent that column and then another column of twos so bring down another two to represent that column times we have one two here but it is a column so bring down a two times another 2 here times another two here so we end up with three times seven times two times two times two times two times two and by multiplying those numbers we get the least common multiple now there are different ways to go about multiplying these numbers for example you can start with 3 times 7 and work your way from left to right I'm going to start with this group of five twos right here so we have two times two times two times two times two two to the fifth power we have two expanded out five times and multiplied so two times two is four times two is eight times two is sixteen times two is thirty-two then we can bring down our seven and three now again there are different ways to go about multiplying these numbers I'm just going to work from left to right so I'll do three times seven next which is twenty one and then we have 21 times 32 for our last step now I'm not sure what 21 times 32 is so I need to work this out off to the side so 32 times 21. I put the larger number in value on top let's multiply 1 times 2 is 2 1 times 3 is 3. we are done with this one and now we need that zero two times two is four and then 2 times 3 is 6. now we add 32 plus 640. two plus zero is two three plus four is seven and then we have that six so six hundred seventy two and that's our least common multiple so I'll put an arrow there so 3 times 7 times 2 times 2 times 2 times 2 times 2 equals 672. so the LCM the least common multiple of 21 28 and 32 I don't know is 600 72. so there's how to find the least common multiple of three numbers using prime factorization and that's a wrap for the least common multiple portion of this video so there you have it there's a complete guide to greatest common factor and least common multiple I hope that helped thanks so much for watching until next time peace