Q:

What is the LCM of 75 and 135?

Accepted Solution

A:
Solution: The LCM of 75 and 135 is 675 Methods How to find the LCM of 75 and 135 using Prime Factorization One way to find the LCM of 75 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 75? What are the Factors of 135? Here is the prime factorization of 75: 3 1 × 5 2 3^1 × 5^2 3 1 × 5 2 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: 3, 5 3 3 × 5 2 = 675 3^3 × 5^2 = 675 3 3 × 5 2 = 675 Through this we see that the LCM of 75 and 135 is 675. How to Find the LCM of 75 and 135 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 75 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, 75 and 135: What are the Multiples of 75? What are the Multiples of 135? Let’s take a look at the first 10 multiples for each of these numbers, 75 and 135: First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750 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 75 and 135 are 675, 1350, 2025. Because 675 is the smallest, it is the least common multiple. The LCM of 75 and 135 is 675. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 40 and 31? What is the LCM of 103 and 109? What is the LCM of 132 and 14? What is the LCM of 127 and 2? What is the LCM of 117 and 49?