Q:

What is the LCM of 72 and 39?

Accepted Solution

A:
Solution: The LCM of 72 and 39 is 936 Methods How to find the LCM of 72 and 39 using Prime Factorization One way to find the LCM of 72 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 72? What are the Factors of 39? Here is the prime factorization of 72: 2 3 × 3 2 2^3 × 3^2 2 3 × 3 2 And this is the prime factorization of 39: 3 1 × 1 3 1 3^1 × 13^1 3 1 × 1 3 1 When 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, 13 2 3 × 3 2 × 1 3 1 = 936 2^3 × 3^2 × 13^1 = 936 2 3 × 3 2 × 1 3 1 = 936 Through this we see that the LCM of 72 and 39 is 936. How to Find the LCM of 72 and 39 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 72 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, 72 and 39: What are the Multiples of 72? What are the Multiples of 39? Let’s take a look at the first 10 multiples for each of these numbers, 72 and 39: First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720 First 10 Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390 You 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 72 and 39 are 936, 1872, 2808. Because 936 is the smallest, it is the least common multiple. The LCM of 72 and 39 is 936. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 93 and 29? What is the LCM of 117 and 81? What is the LCM of 75 and 80? What is the LCM of 104 and 122? What is the LCM of 16 and 118?