Q:

What is the LCM of 135 and 123?

Accepted Solution

A:
Solution: The LCM of 135 and 123 is 5535 Methods How to find the LCM of 135 and 123 using Prime Factorization One way to find the LCM of 135 and 123 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 123? Here is the prime factorization of 135: 3 3 × 5 1 3^3 × 5^1 3 3 × 5 1 And this is the prime factorization of 123: 3 1 × 4 1 1 3^1 × 41^1 3 1 × 4 1 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, 41 3 3 × 5 1 × 4 1 1 = 5535 3^3 × 5^1 × 41^1 = 5535 3 3 × 5 1 × 4 1 1 = 5535 Through this we see that the LCM of 135 and 123 is 5535. How to Find the LCM of 135 and 123 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 135 and 123 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 123: What are the Multiples of 135? What are the Multiples of 123? Let’s take a look at the first 10 multiples for each of these numbers, 135 and 123: First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350 First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230 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 123 are 5535, 11070, 16605. Because 5535 is the smallest, it is the least common multiple. The LCM of 135 and 123 is 5535. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 50 and 55? What is the LCM of 78 and 126? What is the LCM of 80 and 103? What is the LCM of 47 and 1? What is the LCM of 45 and 73?