The lowest common multiple or LCM, is the smallest positive integer that is divisible by two numbers. In other words it is the smallest number that both numbers will divide into.Follow these steps to help you find the least common multiple or LCM
Lowest Common Multiple
Complete a factor tree and factor down until you only have prime numbers remaining
Multiply the list of prime numbers together. The sum will be your LCM
Make a list of your prime numbers. If a number is on both lists you can add one number to the list. See number 5 in the example.
Ok let’s get started. I will do my factor trees, four times five get to prime factorization and then make my list. Five cross it out, three cross one out, and two cross the other one out. So I multiply all this together, so my answer is sixty. Ok now let’s slow it down and go over the rules. Rule number one, complete your prime factorization. That just means we create a factor tree, and break it down to the smallest factors. The second step is to write a list of all of these factors. We then will take that list and cross out one from each of the two of the numbers that we are finding the least common multiple for, and then we will multiple those factors together,to get our answer. The most confusing part is the middle part. Let’s go back and break it down again. Ok we have fifteen and we have twenty. We want to find the smallest number that fifteen and twenty divide into to. So it will be a number greater that fifteen and twenty. Step one, I write my prime factorization. So fifteen is fairly simple to factor, five times three. Twenty breaks down into four times five and then four is two times two. So our prime factorization is two times five. Now the second step is a little confusing. I’m going to create a list that has all of these factors represented. Notice that five is in both lists so I’m going to write my five and I’m going to cross out my five on this list and one five on that list. Now I have a three over here and I have to account for that three and then the next number I have to have represented is a two. Now, let’s multiple together three times five is fifteen, two times two is four, four times fifteen is sixty so that is my least common multiple.