HCF (Highest Common Factor) and LCM (Least Common Multiple) are essential concepts in quantitative aptitude.
Important for bank, MBA, and placement tests.
Good command over these concepts improves scores.
HCF
Definition
HCF is the highest number that divides two or more numbers completely without leaving a remainder.
Also known as GCD (Greatest Common Divisor).
Example of Calculating HCF
Finding HCF of 42, 54, and 36.
Simplification method:
Start dividing numbers by common factors (starting from 2).
Continue until no further divisions are possible.
Multiply the factors from the left side to get the HCF.
For the example: HCF of 42, 54, and 36 is 6.
Tips for Finding HCF Quickly
Use observation with familiar numbers to identify common factors.
Example: HCF of 18, 24, and 30 is 6 by observation without drawing tables.
LCM
Definition
LCM is the smallest number that is a multiple of two or more numbers.
Example of Calculating LCM
Finding LCM of 2 and 3:
List multiples of 2 and 3 (6 is the smallest common multiple).
Simplification method:
Divide by common factors until reaching 1.
For example: LCM of 250, 100, and 125 is 500.
Tips for Finding LCM Quickly
If one number is a multiple of another, only consider the larger number.
Example: For 12, 36, 72, and 144, LCM is 144 since 144 is a multiple of all.
HCF and LCM of Fractions
To find LCM of fractions: LCM of numerators divided by HCF of denominators.
To find HCF of fractions: HCF of numerators divided by LCM of denominators.
Common Problems and Techniques
Finding Greatest Number
When finding the greatest number that divides two or more numbers leaving specific remainders, adjust the numbers by subtracting the remainders.
Example: For 17, 42, and 93 with remainders 4, 3, and 15 respectively, the adjusted numbers are 13, 39, and 78, and the HCF of these gives the answer.
Least Number with Remainders
For finding the least number that leaves the same remainder when divided by several numbers, first find the LCM and add the common remainder.
Sum of Two Numbers with HCF
If the sum of two numbers is known along with their HCF, the numbers can be expressed as multiples of their HCF.
Analyze pairs of multiples to find valid combinations.
Conclusion
HCF and LCM are critical for solving problems in quantitative aptitude.
Practice and familiarity with concepts can greatly enhance performance in exams.
For more practice questions, visit career.com.
Additional Remarks
The lecture emphasized on the importance of understanding HCF and LCM, providing both theoretical and practical examples, tips, and tricks for efficient calculations.