Q:

What is the LCM of 52 and 107?

Accepted Solution

A:
Solution: The LCM of 52 and 107 is 5564 Methods How to find the LCM of 52 and 107 using Prime Factorization One way to find the LCM of 52 and 107 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 52? What are the Factors of 107? Here is the prime factorization of 52: 2 2 × 1 3 1 2^2 × 13^1 2 2 × 1 3 1 And this is the prime factorization of 107: 10 7 1 107^1 10 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, 13, 107 2 2 × 1 3 1 × 10 7 1 = 5564 2^2 × 13^1 × 107^1 = 5564 2 2 × 1 3 1 × 10 7 1 = 5564 Through this we see that the LCM of 52 and 107 is 5564. How to Find the LCM of 52 and 107 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 52 and 107 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, 52 and 107: What are the Multiples of 52? What are the Multiples of 107? Let’s take a look at the first 10 multiples for each of these numbers, 52 and 107: First 10 Multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520 First 10 Multiples of 107: 107, 214, 321, 428, 535, 642, 749, 856, 963, 1070 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 52 and 107 are 5564, 11128, 16692. Because 5564 is the smallest, it is the least common multiple. The LCM of 52 and 107 is 5564. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 110 and 61? What is the LCM of 75 and 99? What is the LCM of 118 and 105? What is the LCM of 102 and 80? What is the LCM of 40 and 133?