Differentiate between GCFs and LCMs in Common Core Math

By Christopher Danielson

In Common Core math, sixth graders apply their knowledge of factors and multiples to look for the greatest common factor (or GCF) of two numbers and the least common multiple (LCM) of two numbers.

The greatest common factor of two numbers is the largest number that is a factor of both numbers. The first step in thinking about GCF is to think about common factors. For example, think about the numbers 4 and 10. The factors of 4 are 1, 2, and 4. The factors of 10 are 1, 2, 5, and 10. The common factors of these numbers are 1 and 2. The greatest common factor is 2 because it’s the biggest number on the list of common factors. So you can say that the GCF of 4 and 10 is 2.

The least common multiple is the smallest (or least) number that is a multiple of both numbers. The first step in thinking about LCM is to think about common multiples. For example, think again about the numbers 4 and 10. The multiples of 4 are 4, 8, 12, 16, 20, 24, and so on (notice that these are the numbers you say when you skip count by 4, starting at 4 — skip counting is another way to think about the multiples of a number). The multiples of 10 are 10, 20, 30, 40, and so on. If you continue both of these lists far enough, there turn out to be many numbers on both lists: 20, 40, 60, and 80 are all examples of common multiples of 4 and 10. The least common multiple is the smallest number on that list: 20. So you can say that the LCM of 4 and 10 is 20.