List Method

GCF = Greatest Common Factor

GCF describes itself backwards

1. List the factors for the numbers
2. Find the common factors
3. Identify the greatest (biggest) factor the two numbers have in common.

EXAMPLE:     GCF(16,28)

List the factors of 16: 1,2,4,8,16
List the factors of 28: 1,2,4,7,14,28

The common factors are 1, 2, and 4
The greatest common factor is 4

So the GCF(16,28) = 4

LCM = Least Common Multiple

LCM also describes itself backwards

1. List the multiples of the numbers
2. Find the common multiples
3. Identify the least (smallest) multiple the two numbers have in common.

EXAMPLE:     LCM(12,18)

Multiples of 12: 12,24,36,48,60,72 and so on
Multiples of 18: 18,36,54,72,90 and so on

The common multiples are 36, 72, and so on
The least common multiple is 36

So the LCM(12,18) = 36

The biggest drawback for this method is that the LCM may require a very large list of multiples before the common multiples show up.

This method is great for finding the GCF but you may want to also know another method for finding the LCM.