Q:

What is the LCM of 138 and 54?

Accepted Solution

A:
Solution: The LCM of 138 and 54 is 1242 Methods How to find the LCM of 138 and 54 using Prime Factorization One way to find the LCM of 138 and 54 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 138? What are the Factors of 54? Here is the prime factorization of 138: 2 1 × 3 1 × 2 3 1 2^1 × 3^1 × 23^1 2 1 × 3 1 × 2 3 1 And this is the prime factorization of 54: 2 1 × 3 3 2^1 × 3^3 2 1 × 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: 2, 3, 23 2 1 × 3 3 × 2 3 1 = 1242 2^1 × 3^3 × 23^1 = 1242 2 1 × 3 3 × 2 3 1 = 1242 Through this we see that the LCM of 138 and 54 is 1242. How to Find the LCM of 138 and 54 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 138 and 54 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, 138 and 54: What are the Multiples of 138? What are the Multiples of 54? Let’s take a look at the first 10 multiples for each of these numbers, 138 and 54: First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380 First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540 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 138 and 54 are 1242, 2484, 3726. Because 1242 is the smallest, it is the least common multiple. The LCM of 138 and 54 is 1242. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 84 and 106? What is the LCM of 55 and 17? What is the LCM of 3 and 107? What is the LCM of 125 and 10? What is the LCM of 60 and 2?