Q:

What is the LCM of 57 and 112?

Accepted Solution

A:
Solution: The LCM of 57 and 112 is 6384 Methods How to find the LCM of 57 and 112 using Prime Factorization One way to find the LCM of 57 and 112 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 57? What are the Factors of 112? Here is the prime factorization of 57: 3 1 × 1 9 1 3^1 × 19^1 3 1 × 1 9 1 And this is the prime factorization of 112: 2 4 × 7 1 2^4 × 7^1 2 4 × 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: 3, 19, 2, 7 2 4 × 3 1 × 7 1 × 1 9 1 = 6384 2^4 × 3^1 × 7^1 × 19^1 = 6384 2 4 × 3 1 × 7 1 × 1 9 1 = 6384 Through this we see that the LCM of 57 and 112 is 6384. How to Find the LCM of 57 and 112 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 57 and 112 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, 57 and 112: What are the Multiples of 57? What are the Multiples of 112? Let’s take a look at the first 10 multiples for each of these numbers, 57 and 112: First 10 Multiples of 57: 57, 114, 171, 228, 285, 342, 399, 456, 513, 570 First 10 Multiples of 112: 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120 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 57 and 112 are 6384, 12768, 19152. Because 6384 is the smallest, it is the least common multiple. The LCM of 57 and 112 is 6384. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 42 and 137? What is the LCM of 82 and 19? What is the LCM of 9 and 109? What is the LCM of 97 and 16? What is the LCM of 75 and 84?