Q:

What is the LCM of 96 and 39?

Accepted Solution

A:
Solution: The LCM of 96 and 39 is 1248MethodsHow to find the LCM of 96 and 39 using Prime FactorizationOne way to find the LCM of 96 and 39 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:What are the Factors of 96?What are the Factors of 39?Here is the prime factorization of 96:25×312^5 × 3^125×31And this is the prime factorization of 39:31×1313^1 × 13^131×131When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 2, 3, 1325×31×131=12482^5 × 3^1 × 13^1 = 124825×31×131=1248Through this we see that the LCM of 96 and 39 is 1248.How to Find the LCM of 96 and 39 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 96 and 39 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number. Let’s take a look at the multiples for each of these numbers, 96 and 39:What are the Multiples of 96?What are the Multiples of 39?Let’s take a look at the first 10 multiples for each of these numbers, 96 and 39:First 10 Multiples of 96: 96, 192, 288, 384, 480, 576, 672, 768, 864, 960First 10 Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 96 and 39 are 1248, 2496, 3744. Because 1248 is the smallest, it is the least common multiple.The LCM of 96 and 39 is 1248.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 5 and 53?What is the LCM of 71 and 20?What is the LCM of 32 and 37?What is the LCM of 48 and 23?What is the LCM of 124 and 18?