Q:

What is the LCM of 21 and 137?

Accepted Solution

A:
Solution: The LCM of 21 and 137 is 2877 Methods How to find the LCM of 21 and 137 using Prime Factorization One way to find the LCM of 21 and 137 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 21? What are the Factors of 137? Here is the prime factorization of 21: 3 1 × 7 1 3^1 × 7^1 3 1 × 7 1 And this is the prime factorization of 137: 13 7 1 137^1 13 7 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, 7, 137 3 1 × 7 1 × 13 7 1 = 2877 3^1 × 7^1 × 137^1 = 2877 3 1 × 7 1 × 13 7 1 = 2877 Through this we see that the LCM of 21 and 137 is 2877. How to Find the LCM of 21 and 137 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 21 and 137 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, 21 and 137: What are the Multiples of 21? What are the Multiples of 137? Let’s take a look at the first 10 multiples for each of these numbers, 21 and 137: First 10 Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210 First 10 Multiples of 137: 137, 274, 411, 548, 685, 822, 959, 1096, 1233, 1370 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 21 and 137 are 2877, 5754, 8631. Because 2877 is the smallest, it is the least common multiple. The LCM of 21 and 137 is 2877. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 14 and 118? What is the LCM of 101 and 134? What is the LCM of 96 and 25? What is the LCM of 94 and 112? What is the LCM of 12 and 40?