Q:

What is the LCM of 117 and 69?

Accepted Solution

A:
Solution: The LCM of 117 and 69 is 2691 Methods How to find the LCM of 117 and 69 using Prime Factorization One way to find the LCM of 117 and 69 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 117? What are the Factors of 69? Here is the prime factorization of 117: 3 2 × 1 3 1 3^2 × 13^1 3 2 × 1 3 1 And this is the prime factorization of 69: 3 1 × 2 3 1 3^1 × 23^1 3 1 × 2 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: 3, 13, 23 3 2 × 1 3 1 × 2 3 1 = 2691 3^2 × 13^1 × 23^1 = 2691 3 2 × 1 3 1 × 2 3 1 = 2691 Through this we see that the LCM of 117 and 69 is 2691. How to Find the LCM of 117 and 69 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 117 and 69 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, 117 and 69: What are the Multiples of 117? What are the Multiples of 69? Let’s take a look at the first 10 multiples for each of these numbers, 117 and 69: First 10 Multiples of 117: 117, 234, 351, 468, 585, 702, 819, 936, 1053, 1170 First 10 Multiples of 69: 69, 138, 207, 276, 345, 414, 483, 552, 621, 690 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 117 and 69 are 2691, 5382, 8073. Because 2691 is the smallest, it is the least common multiple. The LCM of 117 and 69 is 2691. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 79 and 63? What is the LCM of 123 and 22? What is the LCM of 87 and 15? What is the LCM of 118 and 86? What is the LCM of 98 and 33?