Q:

What is the LCM of 76 and 109?

Accepted Solution

A:
Solution: The LCM of 76 and 109 is 8284 Methods How to find the LCM of 76 and 109 using Prime Factorization One way to find the LCM of 76 and 109 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 76? What are the Factors of 109? Here is the prime factorization of 76: 2 2 × 1 9 1 2^2 × 19^1 2 2 × 1 9 1 And this is the prime factorization of 109: 10 9 1 109^1 10 9 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, 19, 109 2 2 × 1 9 1 × 10 9 1 = 8284 2^2 × 19^1 × 109^1 = 8284 2 2 × 1 9 1 × 10 9 1 = 8284 Through this we see that the LCM of 76 and 109 is 8284. How to Find the LCM of 76 and 109 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 76 and 109 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, 76 and 109: What are the Multiples of 76? What are the Multiples of 109? Let’s take a look at the first 10 multiples for each of these numbers, 76 and 109: First 10 Multiples of 76: 76, 152, 228, 304, 380, 456, 532, 608, 684, 760 First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090 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 76 and 109 are 8284, 16568, 24852. Because 8284 is the smallest, it is the least common multiple. The LCM of 76 and 109 is 8284. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 147 and 80? What is the LCM of 15 and 13? What is the LCM of 29 and 50? What is the LCM of 30 and 126? What is the LCM of 108 and 17?