Q:

What is the LCM of 116 and 67?

Accepted Solution

A:
Solution: The LCM of 116 and 67 is 7772 Methods How to find the LCM of 116 and 67 using Prime Factorization One way to find the LCM of 116 and 67 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 116? What are the Factors of 67? Here is the prime factorization of 116: 2 2 × 2 9 1 2^2 × 29^1 2 2 × 2 9 1 And this is the prime factorization of 67: 6 7 1 67^1 6 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, 29, 67 2 2 × 2 9 1 × 6 7 1 = 7772 2^2 × 29^1 × 67^1 = 7772 2 2 × 2 9 1 × 6 7 1 = 7772 Through this we see that the LCM of 116 and 67 is 7772. How to Find the LCM of 116 and 67 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 116 and 67 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, 116 and 67: What are the Multiples of 116? What are the Multiples of 67? Let’s take a look at the first 10 multiples for each of these numbers, 116 and 67: First 10 Multiples of 116: 116, 232, 348, 464, 580, 696, 812, 928, 1044, 1160 First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670 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 116 and 67 are 7772, 15544, 23316. Because 7772 is the smallest, it is the least common multiple. The LCM of 116 and 67 is 7772. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 129 and 83? What is the LCM of 79 and 39? What is the LCM of 46 and 82? What is the LCM of 100 and 149? What is the LCM of 107 and 112?