Q:

What is the LCM of 135 and 27?

Accepted Solution

A:
Solution: The LCM of 135 and 27 is 135 Methods How to find the LCM of 135 and 27 using Prime Factorization One way to find the LCM of 135 and 27 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 135? What are the Factors of 27? Here is the prime factorization of 135: 3 3 Γ— 5 1 3^3 Γ— 5^1 3 3 Γ— 5 1 And this is the prime factorization of 27: 3 3 3^3 3 3 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 Γ— 5 1 = 135 3^3 Γ— 5^1 = 135 3 3 Γ— 5 1 = 135 Through this we see that the LCM of 135 and 27 is 135. How to Find the LCM of 135 and 27 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 135 and 27 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, 135 and 27: What are the Multiples of 135? What are the Multiples of 27? Let’s take a look at the first 10 multiples for each of these numbers, 135 and 27: First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350 First 10 Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270 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 135 and 27 are 135, 270, 405. Because 135 is the smallest, it is the least common multiple. The LCM of 135 and 27 is 135. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 133 and 119? What is the LCM of 23 and 71? What is the LCM of 58 and 1? What is the LCM of 110 and 25? What is the LCM of 95 and 81?