Q:

What is the LCM of 136 and 85?

Accepted Solution

A:
Solution: The LCM of 136 and 85 is 680 Methods How to find the LCM of 136 and 85 using Prime Factorization One way to find the LCM of 136 and 85 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 136? What are the Factors of 85? Here is the prime factorization of 136: 2 3 Γ— 1 7 1 2^3 Γ— 17^1 2 3 Γ— 1 7 1 And this is the prime factorization of 85: 5 1 Γ— 1 7 1 5^1 Γ— 17^1 5 1 Γ— 1 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, 17, 5 2 3 Γ— 5 1 Γ— 1 7 1 = 680 2^3 Γ— 5^1 Γ— 17^1 = 680 2 3 Γ— 5 1 Γ— 1 7 1 = 680 Through this we see that the LCM of 136 and 85 is 680. How to Find the LCM of 136 and 85 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 136 and 85 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, 136 and 85: What are the Multiples of 136? What are the Multiples of 85? Let’s take a look at the first 10 multiples for each of these numbers, 136 and 85: First 10 Multiples of 136: 136, 272, 408, 544, 680, 816, 952, 1088, 1224, 1360 First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850 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 136 and 85 are 680, 1360, 2040. Because 680 is the smallest, it is the least common multiple. The LCM of 136 and 85 is 680. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 39 and 125? What is the LCM of 38 and 140? What is the LCM of 1 and 94? What is the LCM of 24 and 25? What is the LCM of 48 and 121?