Q:

What is the LCM of 45 and 117?

Accepted Solution

A:
Solution: The LCM of 45 and 117 is 585 Methods How to find the LCM of 45 and 117 using Prime Factorization One way to find the LCM of 45 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 45? What are the Factors of 117? Here is the prime factorization of 45: 3 2 × 5 1 3^2 × 5^1 3 2 × 5 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: 3, 5, 13 3 2 × 5 1 × 1 3 1 = 585 3^2 × 5^1 × 13^1 = 585 3 2 × 5 1 × 1 3 1 = 585 Through this we see that the LCM of 45 and 117 is 585. How to Find the LCM of 45 and 117 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 45 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, 45 and 117: What are the Multiples of 45? What are the Multiples of 117? Let’s take a look at the first 10 multiples for each of these numbers, 45 and 117: First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450 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 45 and 117 are 585, 1170, 1755. Because 585 is the smallest, it is the least common multiple. The LCM of 45 and 117 is 585. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 86 and 35? What is the LCM of 5 and 108? What is the LCM of 9 and 150? What is the LCM of 34 and 1? What is the LCM of 39 and 72?