Math with Mr. Jay: A Guide to Greatest Common Factor (GCF) and Least Common Multiple (LCM)

Introduction

• Overview of the topics to cover:
  • Greatest Common Factor (GCF)
  • Least Common Multiple (LCM)
• Strategies for working with numbers, including three numbers.

Greatest Common Factor (GCF)

Basics of GCF

• Factors: Numbers that can be multiplied together to get another number.
• Common Factors: Factors that two numbers share.
• Greatest Common Factor (GCF): The largest factor that two or more numbers share.

Finding GCF

Example: 12 and 18

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• Common Factors: 1, 2, 3, 6
• GCF: 6

Additional Examples

• 16 and 24:
  • Factors: 1, 2, 4, 8, 16
  • GCF: 8
• 15 and 35:
  • Factors: 1, 3, 5, 15
  • GCF: 5

Strategies for GCF

Prime Factorization

• Useful for larger numbers.
• Example 1: 63 and 84
  • Prime Factorization: 63 (3x3x7), 84 (2x2x3x7)
  • Common Prime Factors: 3, 7
  • GCF: 21
• Example 2: 48 and 72
  • Prime Factorization: 48 (2x2x2x2x3), 72 (2x2x2x3x3)
  • Common Prime Factors: 2, 2, 2, 3
  • GCF: 24

GCF of Three Numbers

• Example: 27, 9, 18
  • Common Factors: 1, 3, 9
  • GCF: 9
• Using Prime Factorization for larger numbers.

Least Common Multiple (LCM)

Basics of LCM

• Multiples: The result of multiplying a number by an integer.
• Common Multiples: Multiples that two or more numbers share.
• Least Common Multiple (LCM): The smallest multiple that two or more numbers share.

Finding LCM

Example: 6 and 15

• Multiples of 6: 6, 12, 18, 24, 30
• Multiples of 15: 15, 30, 45, 60
• Common Multiples: 30, 60
• LCM: 30

Additional Examples

• 9 and 12:
  • LCM: 36
• 10 and 25:
  • LCM: 50

Strategies for LCM

Prime Factorization

• Useful for larger numbers.
• Example 1: 15 and 27
  • Prime Factorization: 15 (3x5), 27 (3x3x3)
  • LCM: 135
• Example 2: 28 and 52
  • Prime Factorization: 28 (2x2x7), 52 (2x2x13)
  • LCM: 364

LCM of Three Numbers

• Example: 5, 8, 20
  • LCM: 40
• Using Prime Factorization for larger numbers.

Conclusion

• Comprehensive coverage of GCF and LCM.
• Various strategies to approach problems with different levels of complexity.
• Encouragement to practice for improved understanding and efficiency.