How to Find the Least Common Multiple Using Prime Factorization Multiplication Tips

hi I'm Jimmy Chang and we're here to talk about how to find the least common multiple using prime factorization now this is very important concept when it comes to pre-algebra and Elementary algebra courses because it really lays the foundation to help you find the least common denominator which is actually an application of the least common multiple so it involves using factoring trees and we'll see how this is used right now suppose you want to find the least common multiple the LCM of these numbers 12 12 and 18 now the pattern is pretty consistent in that you want to take both numbers and you want to create factoring trees out of both of them now with 12 you break it up this way you can think of any two numbers that multiply to give you 12 and you'll be good to go so most people often think of 4 * 3 now what you do after that is see if you can break down each number further if possible now four four can be thought of as 2 * 2 3 that's about as good as it gets so the factorization of 12 is really 2 * 2 * 3 you're going to leave that aside for right now you can do the same thing with 18 you're going to break down 18 and as you know any first way that you want any two numbers multiply to give you 18 some people will think of 9 * 2 and go from there now 9 can be thought of as 3 * 3 but the two is about as good as it gets so 18 can be written in order 2 * 3 time 3 now when it comes to finding the least common multiple what you want to think about is look at the number of factors and see which number has the most of each number and circle it from there so for example between 12 and 18 who has the most twos as you can tell the 12 has more twos and it's got two of them so you're going to circle those two twos that's going to be part of your least common multiple next you move on to see if who has the most threes in circle that amount now between the 12 and 18 the 18 has more thre so you're going to circle those two threes now if you ever have tie when it comes to LCM for example if both of them had two threes you just circle one pair so the three and the three is part of the least common multiple and then you multiply what you have from here and that's going to be the LCM 2 * 2 is 4 3 * 3 is 9 and 4 * 9 is going to be 36 which is going to give you the least common multiple so the bottom line is when it comes to prime factorization you break up each number as much as possible and then you Circle who has the most number of factors from each and you'll be good to go and after you multiply them you'll have your least common multiple so I'm Jimmy Chang and that's how to find the least common multiple using prime factorization