Q:

What is the LCM of 57 and 61?

Accepted Solution

A:
Solution: The LCM of 57 and 61 is 3477 Methods How to find the LCM of 57 and 61 using Prime Factorization One way to find the LCM of 57 and 61 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 61? 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 61: 6 1 1 61^1 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: 3, 19, 61 3 1 × 1 9 1 × 6 1 1 = 3477 3^1 × 19^1 × 61^1 = 3477 3 1 × 1 9 1 × 6 1 1 = 3477 Through this we see that the LCM of 57 and 61 is 3477. How to Find the LCM of 57 and 61 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 57 and 61 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 61: What are the Multiples of 57? What are the Multiples of 61? Let’s take a look at the first 10 multiples for each of these numbers, 57 and 61: First 10 Multiples of 57: 57, 114, 171, 228, 285, 342, 399, 456, 513, 570 First 10 Multiples of 61: 61, 122, 183, 244, 305, 366, 427, 488, 549, 610 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 61 are 3477, 6954, 10431. Because 3477 is the smallest, it is the least common multiple. The LCM of 57 and 61 is 3477. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 32 and 68? What is the LCM of 72 and 70? What is the LCM of 86 and 13? What is the LCM of 141 and 66? What is the LCM of 80 and 128?