What is the difference between finding Least Common Multiple and greatest common factor using prime fractionation?

Answer 1

The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers. The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder. Factors go into numbers, numbers go into multiples.

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Combine the factors, eliminating duplicates.

2 x 3 x 5 x 7 = 210, the LCM

Check it.

30 x 42 = 1260

210 x 6 = 1260

It checks.

Answer 2

All composite numbers can be expressed as unique products of prime numbers. This is called a prime factorization.

The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers.

Answer 3

A greatest common factor (GCF) is the largest factor of two numbers. For example, 12 and 36:The factors of 12 are 1, 2, 3, 4, 6, 12.The factors of 36 are 1, 2, 3, 4, 6, 8, 12, 18, 36.The GCF is 12.Prime factorization is factoring a number until all the factors are prime numbers. For example, 80:Start with any factor pair of 80:2 x 402 x 2 x 202 x 2 x 2 x 102 x 2 x 2 x 2 x 5.