Q:

What is the LCM of 116 and 139?

Accepted Solution

A:
Solution: The LCM of 116 and 139 is 16124 Methods How to find the LCM of 116 and 139 using Prime Factorization One way to find the LCM of 116 and 139 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 139? 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 139: 13 9 1 139^1 13 9 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, 139 2 2 × 2 9 1 × 13 9 1 = 16124 2^2 × 29^1 × 139^1 = 16124 2 2 × 2 9 1 × 13 9 1 = 16124 Through this we see that the LCM of 116 and 139 is 16124. How to Find the LCM of 116 and 139 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 116 and 139 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 139: What are the Multiples of 116? What are the Multiples of 139? Let’s take a look at the first 10 multiples for each of these numbers, 116 and 139: First 10 Multiples of 116: 116, 232, 348, 464, 580, 696, 812, 928, 1044, 1160 First 10 Multiples of 139: 139, 278, 417, 556, 695, 834, 973, 1112, 1251, 1390 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 139 are 16124, 32248, 48372. Because 16124 is the smallest, it is the least common multiple. The LCM of 116 and 139 is 16124. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 107 and 138? What is the LCM of 120 and 57? What is the LCM of 91 and 29? What is the LCM of 70 and 2? What is the LCM of 114 and 23?