Q:

What is the LCM of 117 and 10?

Accepted Solution

A:
Solution: The LCM of 117 and 10 is 1170 Methods How to find the LCM of 117 and 10 using Prime Factorization One way to find the LCM of 117 and 10 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 10? 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 10: 2 1 × 5 1 2^1 × 5^1 2 1 × 5 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, 2, 5 2 1 × 3 2 × 5 1 × 1 3 1 = 1170 2^1 × 3^2 × 5^1 × 13^1 = 1170 2 1 × 3 2 × 5 1 × 1 3 1 = 1170 Through this we see that the LCM of 117 and 10 is 1170. How to Find the LCM of 117 and 10 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 117 and 10 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 10: What are the Multiples of 117? What are the Multiples of 10? Let’s take a look at the first 10 multiples for each of these numbers, 117 and 10: First 10 Multiples of 117: 117, 234, 351, 468, 585, 702, 819, 936, 1053, 1170 First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 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 10 are 1170, 2340, 3510. Because 1170 is the smallest, it is the least common multiple. The LCM of 117 and 10 is 1170. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 104 and 128? What is the LCM of 109 and 31? What is the LCM of 53 and 76? What is the LCM of 66 and 92? What is the LCM of 149 and 81?