Q:

What is the LCM of 6 and 72?

Accepted Solution

A:
Solution: The LCM of 6 and 72 is 72 Methods How to find the LCM of 6 and 72 using Prime Factorization One way to find the LCM of 6 and 72 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 6? What are the Factors of 72? Here is the prime factorization of 6: 2 1 × 3 1 2^1 × 3^1 2 1 × 3 1 And this is the prime factorization of 72: 2 3 × 3 2 2^3 × 3^2 2 3 × 3 2 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 2 3 × 3 2 = 72 2^3 × 3^2 = 72 2 3 × 3 2 = 72 Through this we see that the LCM of 6 and 72 is 72. How to Find the LCM of 6 and 72 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 6 and 72 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, 6 and 72: What are the Multiples of 6? What are the Multiples of 72? Let’s take a look at the first 10 multiples for each of these numbers, 6 and 72: First 10 Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720 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 6 and 72 are 72, 144, 216. Because 72 is the smallest, it is the least common multiple. The LCM of 6 and 72 is 72. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 126 and 75? What is the LCM of 136 and 7? What is the LCM of 48 and 94? What is the LCM of 40 and 2? What is the LCM of 73 and 121?