Assignment: 09-Least Common Multiple
Practice: 10-GCF LCM Practice
Practice: 11-GCF LCM Practice
Much like the GCF, if you understand the meaning of the words in Least Common Multiple, LCM, then you know what you’re looking for. Least meaning smallest, common meaning same, and multiple being a number you can get by multiplying by it. If we were to take our previous numbers, 12 and 20, and ask for the LCM of them instead, it would be 60. There are three different ways we can find this, the last one being the easiest in my opinion. First you could list out the multiples of the larger number. Once you get to a multiple that would be the same for both, you’ve found it. Listing multiples is like skip counting by that number.
20: 20, 40, 60
12 does not go into 20, so we keep listing. Same with 40. However, 12 does go into 60, so it’s our LCM. Another way is by finding the prime factorization of both numbers. This one is a little more difficult, but by multiplying by all of the prime factors of each number, you can find it as well. However, if there are common prime factors in each number, you only use that factor once. Here’s the example for 12 and 60:
I much prefer the final method, because once you understand the Cake Method for GCF, it looks exactly the same. The only difference is rather than just multiplying the numbers to the side, you multiply the numbers on the side as well as the numbers on the bottom. Example:
