Q:

What is the LCM of 139 and 109?

Accepted Solution

A:
Solution: The LCM of 139 and 109 is 15151 Methods How to find the LCM of 139 and 109 using Prime Factorization One way to find the LCM of 139 and 109 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 139? What are the Factors of 109? Here is the prime factorization of 139: 13 9 1 139^1 13 9 1 And this is the prime factorization of 109: 10 9 1 109^1 10 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: 139, 109 10 9 1 × 13 9 1 = 15151 109^1 × 139^1 = 15151 10 9 1 × 13 9 1 = 15151 Through this we see that the LCM of 139 and 109 is 15151. How to Find the LCM of 139 and 109 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 139 and 109 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, 139 and 109: What are the Multiples of 139? What are the Multiples of 109? Let’s take a look at the first 10 multiples for each of these numbers, 139 and 109: First 10 Multiples of 139: 139, 278, 417, 556, 695, 834, 973, 1112, 1251, 1390 First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090 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 139 and 109 are 15151, 30302, 45453. Because 15151 is the smallest, it is the least common multiple. The LCM of 139 and 109 is 15151. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 143 and 10? What is the LCM of 128 and 16? What is the LCM of 101 and 98? What is the LCM of 109 and 102? What is the LCM of 59 and 148?