Q:

What is the LCM of 51 and 100?

Accepted Solution

A:
Solution: The LCM of 51 and 100 is 5100 Methods How to find the LCM of 51 and 100 using Prime Factorization One way to find the LCM of 51 and 100 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 51? What are the Factors of 100? Here is the prime factorization of 51: 3 1 Γ— 1 7 1 3^1 Γ— 17^1 3 1 Γ— 1 7 1 And this is the prime factorization of 100: 2 2 Γ— 5 2 2^2 Γ— 5^2 2 2 Γ— 5 2 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, 17, 2, 5 2 2 Γ— 3 1 Γ— 5 2 Γ— 1 7 1 = 5100 2^2 Γ— 3^1 Γ— 5^2 Γ— 17^1 = 5100 2 2 Γ— 3 1 Γ— 5 2 Γ— 1 7 1 = 5100 Through this we see that the LCM of 51 and 100 is 5100. How to Find the LCM of 51 and 100 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 51 and 100 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, 51 and 100: What are the Multiples of 51? What are the Multiples of 100? Let’s take a look at the first 10 multiples for each of these numbers, 51 and 100: First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510 First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 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 51 and 100 are 5100, 10200, 15300. Because 5100 is the smallest, it is the least common multiple. The LCM of 51 and 100 is 5100. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 122 and 90? What is the LCM of 129 and 91? What is the LCM of 24 and 81? What is the LCM of 5 and 141? What is the LCM of 6 and 124?