Q:

What is the LCM of 116 and 39?

Accepted Solution

A:
Solution: The LCM of 116 and 39 is 4524 Methods How to find the LCM of 116 and 39 using Prime Factorization One way to find the LCM of 116 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 116? What are the Factors of 39? Here is the prime factorization of 116: 2 2 × 2 9 1 2^2 × 29^1 2 2 × 2 9 1 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, 29, 3, 13 2 2 × 3 1 × 1 3 1 × 2 9 1 = 4524 2^2 × 3^1 × 13^1 × 29^1 = 4524 2 2 × 3 1 × 1 3 1 × 2 9 1 = 4524 Through this we see that the LCM of 116 and 39 is 4524. How to Find the LCM of 116 and 39 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 116 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, 116 and 39: What are the Multiples of 116? What are the Multiples of 39? Let’s take a look at the first 10 multiples for each of these numbers, 116 and 39: First 10 Multiples of 116: 116, 232, 348, 464, 580, 696, 812, 928, 1044, 1160 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 116 and 39 are 4524, 9048, 13572. Because 4524 is the smallest, it is the least common multiple. The LCM of 116 and 39 is 4524. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 10 and 13? What is the LCM of 24 and 133? What is the LCM of 112 and 110? What is the LCM of 44 and 60? What is the LCM of 38 and 45?