Math Grade 5 Least Common Multiple L C

Math Grade 5 Least Common Multiple (L. C. M. ) & Greatest Common Factor (G. C. F. )

Least Common Multiple Follow the links below as an introduction to: Finding Least Common Multiple by listing multiples Finding L. C. M. using prime factorization

Least Common Multiple Example 1: (Using listing multiples) Find the L. C. M. of 4 and 6 using listing multiples. Multiples of 4: 4 , 8 , 12 , 16 , 20 , 24 , 28 … Multiples of 6: 6 , 12 , 18 , 24 , 30 … The L. C. M. of 4 and 6 is 12.

Example 2: (Using prime factorization) Find the L. C. M. of 4 and 6 using prime factorization. 4 6 2 x 2 2 x 3 4=2 x 2 6=2 x 3 L. C. M. = 2 x 3 = 12 The L. C. M. of 4 and 6 is 12.

Exercises 1. Find the L. C. M. using listing multiples. a. 8 , 12 b. 5 , 7 2. Find the L. C. M. using prime factorization. a. 12 , 24 b. 14 , 20

Greatest Common Factor Follow the links below as an introduction to: Finding Greatest Common Factor by listing factors Finding G. C. F. using prime factorization

Greatest Common Factor Example 1: (Using listing factors) Find the G. C. F. of 4 and 6 using listing factors. Factors of 4: 1 , 2 , 4 Factors of 6: 1 , 2 , 3 , 6 The G. C. F. of 4 and 6 is 2.

Example 2: (Using listing factors) Find the G. C. F. of 6 and 12 using listing factors. Factors of 6: 1 , 2 , 3 , 6 Factors of 12: 1 , 2 , 3 , 4 , 6 , 12 The G. C. F. of 6 and 12 is 6.

Example 3: (Using prime factorization) Find the G. C. F. of 4 and 6 using prime factorization. 4 6 2 x 2 2 x 3 4=2 x 2 6=2 x 3 G. C. F. = 2 The G. C. F. of 4 and 6 is 2.

Example 4: (Using prime factorization) Find the G. C. F. of 4 and 7 using prime factorization. 4 7 2 x 2 1 x 7 4=2 x 2 7= 7 G. C. F. = 1 (since there are no common prime factors) The G. C. F. of 4 and 7 is 1. (4 and 7 are called relatively prime numbers. )

Exercises 1. Find the G. C. F. using listing factors. a. 8 , 12 b. 5 , 7 2. Find the G. C. F. using prime factorization. a. 12 , 24 b. 14 , 20