Least Common Multiple or LCM

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, is do our 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 this middle part. So 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. So step one I write my prime factorization. So fifteen is fairly simple it 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 this is the second step which 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 and then another two I have to represent. 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.