Q:

What is the LCM of 72 and 122?

Accepted Solution

A:
Solution: The LCM of 72 and 122 is 4392 Methods How to find the LCM of 72 and 122 using Prime Factorization One way to find the LCM of 72 and 122 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 122? Here is the prime factorization of 72: 2 3 Γ— 3 2 2^3 Γ— 3^2 2 3 Γ— 3 2 And this is the prime factorization of 122: 2 1 Γ— 6 1 1 2^1 Γ— 61^1 2 1 Γ— 6 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: 2, 3, 61 2 3 Γ— 3 2 Γ— 6 1 1 = 4392 2^3 Γ— 3^2 Γ— 61^1 = 4392 2 3 Γ— 3 2 Γ— 6 1 1 = 4392 Through this we see that the LCM of 72 and 122 is 4392. How to Find the LCM of 72 and 122 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 72 and 122 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 122: What are the Multiples of 72? What are the Multiples of 122? Let’s take a look at the first 10 multiples for each of these numbers, 72 and 122: First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720 First 10 Multiples of 122: 122, 244, 366, 488, 610, 732, 854, 976, 1098, 1220 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 122 are 4392, 8784, 13176. Because 4392 is the smallest, it is the least common multiple. The LCM of 72 and 122 is 4392. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 51 and 127? What is the LCM of 108 and 18? What is the LCM of 49 and 36? What is the LCM of 32 and 29? What is the LCM of 15 and 135?