Q:

What is the LCM of 108 and 135?

Accepted Solution

A:
Solution: The LCM of 108 and 135 is 540 Methods How to find the LCM of 108 and 135 using Prime Factorization One way to find the LCM of 108 and 135 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 108? What are the Factors of 135? Here is the prime factorization of 108: 2 2 × 3 3 2^2 × 3^3 2 2 × 3 3 And this is the prime factorization of 135: 3 3 × 5 1 3^3 × 5^1 3 3 × 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: 2, 3, 5 2 2 × 3 3 × 5 1 = 540 2^2 × 3^3 × 5^1 = 540 2 2 × 3 3 × 5 1 = 540 Through this we see that the LCM of 108 and 135 is 540. How to Find the LCM of 108 and 135 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 108 and 135 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, 108 and 135: What are the Multiples of 108? What are the Multiples of 135? Let’s take a look at the first 10 multiples for each of these numbers, 108 and 135: First 10 Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080 First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350 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 108 and 135 are 540, 1080, 1620. Because 540 is the smallest, it is the least common multiple. The LCM of 108 and 135 is 540. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 128 and 141? What is the LCM of 102 and 84? What is the LCM of 60 and 47? What is the LCM of 50 and 140? What is the LCM of 46 and 31?