Q:

What is the LCM of 68 and 37?

Accepted Solution

A:
Solution: The LCM of 68 and 37 is 2516 Methods How to find the LCM of 68 and 37 using Prime Factorization One way to find the LCM of 68 and 37 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 68? What are the Factors of 37? Here is the prime factorization of 68: 2 2 × 1 7 1 2^2 × 17^1 2 2 × 1 7 1 And this is the prime factorization of 37: 3 7 1 37^1 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, 17, 37 2 2 × 1 7 1 × 3 7 1 = 2516 2^2 × 17^1 × 37^1 = 2516 2 2 × 1 7 1 × 3 7 1 = 2516 Through this we see that the LCM of 68 and 37 is 2516. How to Find the LCM of 68 and 37 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 68 and 37 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, 68 and 37: What are the Multiples of 68? What are the Multiples of 37? Let’s take a look at the first 10 multiples for each of these numbers, 68 and 37: First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680 First 10 Multiples of 37: 37, 74, 111, 148, 185, 222, 259, 296, 333, 370 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 68 and 37 are 2516, 5032, 7548. Because 2516 is the smallest, it is the least common multiple. The LCM of 68 and 37 is 2516. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 105 and 98? What is the LCM of 33 and 121? What is the LCM of 21 and 5? What is the LCM of 81 and 42? What is the LCM of 82 and 110?