Q:

What is the LCM of 134 and 116?

Accepted Solution

A:
Solution: The LCM of 134 and 116 is 7772 Methods How to find the LCM of 134 and 116 using Prime Factorization One way to find the LCM of 134 and 116 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 134? What are the Factors of 116? Here is the prime factorization of 134: 2 1 × 6 7 1 2^1 × 67^1 2 1 × 6 7 1 And this is the prime factorization of 116: 2 2 × 2 9 1 2^2 × 29^1 2 2 × 2 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, 67, 29 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 134 and 116 is 7772. How to Find the LCM of 134 and 116 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 134 and 116 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, 134 and 116: What are the Multiples of 134? What are the Multiples of 116? Let’s take a look at the first 10 multiples for each of these numbers, 134 and 116: First 10 Multiples of 134: 134, 268, 402, 536, 670, 804, 938, 1072, 1206, 1340 First 10 Multiples of 116: 116, 232, 348, 464, 580, 696, 812, 928, 1044, 1160 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 134 and 116 are 7772, 15544, 23316. Because 7772 is the smallest, it is the least common multiple. The LCM of 134 and 116 is 7772. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 107 and 51? What is the LCM of 42 and 77? What is the LCM of 35 and 72? What is the LCM of 19 and 6? What is the LCM of 29 and 10?