I’ve talked about finding the LCM by exploring the multiples of both numbers. Earlier this week, I was asked to figure out how to determine the least common multiple using the prime factorization of both numbers. (It came up on a student’s homework.)
This one is kind of neat, and actually takes less time than the traditional method. Let’s take a look.
We’re going to find the LCM for 12 and 16. So we’ll start by finding the prime factors for both numbers.
12 factors to 2 * 2 * 3
16 factors to 2 * 2 * 2 * 2
Both 12 and 16 have two 2s in their list of factors, so we’ll ignore those. That leaves us with the following factors.
12: 3
16: 2 * 2
To find the least common multiple, we multiply the original number by the remaining factors of the other number.
12 * 2 * 2
16 * 3
If you multiply both lines out, you’ll find they both equal 48. The least common multiple for12 and 16 is 48.
You’ll notice this took a lot less work than the other LCM method, so you might want to try it out yourself the next time you’re staring down a page full of LCM questions.
