Q:

What is the LCM of 109 and 117?

Accepted Solution

A:
Solution: The LCM of 109 and 117 is 12753 Methods How to find the LCM of 109 and 117 using Prime Factorization One way to find the LCM of 109 and 117 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 109? What are the Factors of 117? Here is the prime factorization of 109: 10 9 1 109^1 10 9 1 And this is the prime factorization of 117: 3 2 × 1 3 1 3^2 × 13^1 3 2 × 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: 109, 3, 13 3 2 × 1 3 1 × 10 9 1 = 12753 3^2 × 13^1 × 109^1 = 12753 3 2 × 1 3 1 × 10 9 1 = 12753 Through this we see that the LCM of 109 and 117 is 12753. How to Find the LCM of 109 and 117 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 109 and 117 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, 109 and 117: What are the Multiples of 109? What are the Multiples of 117? Let’s take a look at the first 10 multiples for each of these numbers, 109 and 117: First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090 First 10 Multiples of 117: 117, 234, 351, 468, 585, 702, 819, 936, 1053, 1170 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 109 and 117 are 12753, 25506, 38259. Because 12753 is the smallest, it is the least common multiple. The LCM of 109 and 117 is 12753. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 71 and 45? What is the LCM of 2 and 33? What is the LCM of 146 and 112? What is the LCM of 57 and 60? What is the LCM of 115 and 81?