Q:

What is the LCM of 52 and 10?

Accepted Solution

A:
Solution: The LCM of 52 and 10 is 260 Methods How to find the LCM of 52 and 10 using Prime Factorization One way to find the LCM of 52 and 10 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 10? 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 10: 2 1 × 5 1 2^1 × 5^1 2 1 × 5 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, 5 2 2 × 5 1 × 1 3 1 = 260 2^2 × 5^1 × 13^1 = 260 2 2 × 5 1 × 1 3 1 = 260 Through this we see that the LCM of 52 and 10 is 260. How to Find the LCM of 52 and 10 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 52 and 10 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 10: What are the Multiples of 52? What are the Multiples of 10? Let’s take a look at the first 10 multiples for each of these numbers, 52 and 10: First 10 Multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520 First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 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 10 are 260, 520, 780. Because 260 is the smallest, it is the least common multiple. The LCM of 52 and 10 is 260. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 113 and 141? What is the LCM of 38 and 32? What is the LCM of 28 and 139? What is the LCM of 102 and 129? What is the LCM of 22 and 67?