Q:

What is the LCM of 108 and 74?

Accepted Solution

A:
Solution: The LCM of 108 and 74 is 3996 Methods How to find the LCM of 108 and 74 using Prime Factorization One way to find the LCM of 108 and 74 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 108? What are the Factors of 74? Here is the prime factorization of 108: 2 2 × 3 3 2^2 × 3^3 2 2 × 3 3 And this is the prime factorization of 74: 2 1 × 3 7 1 2^1 × 37^1 2 1 × 3 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, 37 2 2 × 3 3 × 3 7 1 = 3996 2^2 × 3^3 × 37^1 = 3996 2 2 × 3 3 × 3 7 1 = 3996 Through this we see that the LCM of 108 and 74 is 3996. How to Find the LCM of 108 and 74 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 108 and 74 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, 108 and 74: What are the Multiples of 108? What are the Multiples of 74? Let’s take a look at the first 10 multiples for each of these numbers, 108 and 74: First 10 Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080 First 10 Multiples of 74: 74, 148, 222, 296, 370, 444, 518, 592, 666, 740 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 108 and 74 are 3996, 7992, 11988. Because 3996 is the smallest, it is the least common multiple. The LCM of 108 and 74 is 3996. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 24 and 43? What is the LCM of 21 and 35? What is the LCM of 141 and 117? What is the LCM of 102 and 10? What is the LCM of 94 and 53?