Q:

What is the LCM of 109 and 92?

Accepted Solution

A:
Solution: The LCM of 109 and 92 is 10028 Methods How to find the LCM of 109 and 92 using Prime Factorization One way to find the LCM of 109 and 92 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 109? What are the Factors of 92? Here is the prime factorization of 109: 10 9 1 109^1 10 9 1 And this is the prime factorization of 92: 2 2 Γ— 2 3 1 2^2 Γ— 23^1 2 2 Γ— 2 3 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: 109, 2, 23 2 2 Γ— 2 3 1 Γ— 10 9 1 = 10028 2^2 Γ— 23^1 Γ— 109^1 = 10028 2 2 Γ— 2 3 1 Γ— 10 9 1 = 10028 Through this we see that the LCM of 109 and 92 is 10028. How to Find the LCM of 109 and 92 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 109 and 92 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, 109 and 92: What are the Multiples of 109? What are the Multiples of 92? Let’s take a look at the first 10 multiples for each of these numbers, 109 and 92: First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090 First 10 Multiples of 92: 92, 184, 276, 368, 460, 552, 644, 736, 828, 920 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 109 and 92 are 10028, 20056, 30084. Because 10028 is the smallest, it is the least common multiple. The LCM of 109 and 92 is 10028. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 53 and 4? What is the LCM of 75 and 92? What is the LCM of 50 and 117? What is the LCM of 17 and 38? What is the LCM of 102 and 95?