Q:

What is the LCM of 72 and 21?

Accepted Solution

A:
Solution: The LCM of 72 and 21 is 504 Methods How to find the LCM of 72 and 21 using Prime Factorization One way to find the LCM of 72 and 21 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 72? What are the Factors of 21? Here is the prime factorization of 72: 2 3 × 3 2 2^3 × 3^2 2 3 × 3 2 And this is the prime factorization of 21: 3 1 × 7 1 3^1 × 7^1 3 1 × 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: 2, 3, 7 2 3 × 3 2 × 7 1 = 504 2^3 × 3^2 × 7^1 = 504 2 3 × 3 2 × 7 1 = 504 Through this we see that the LCM of 72 and 21 is 504. How to Find the LCM of 72 and 21 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 72 and 21 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, 72 and 21: What are the Multiples of 72? What are the Multiples of 21? Let’s take a look at the first 10 multiples for each of these numbers, 72 and 21: First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720 First 10 Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210 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 72 and 21 are 504, 1008, 1512. Because 504 is the smallest, it is the least common multiple. The LCM of 72 and 21 is 504. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 79 and 109? What is the LCM of 74 and 120? What is the LCM of 116 and 86? What is the LCM of 81 and 146? What is the LCM of 144 and 82?