Q:

What is the LCM of 85 and 17?

Accepted Solution

A:
Solution: The LCM of 85 and 17 is 85 Methods How to find the LCM of 85 and 17 using Prime Factorization One way to find the LCM of 85 and 17 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 85? What are the Factors of 17? Here is the prime factorization of 85: 5 1 × 1 7 1 5^1 × 17^1 5 1 × 1 7 1 And this is the prime factorization of 17: 1 7 1 17^1 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: 5, 17 5 1 × 1 7 1 = 85 5^1 × 17^1 = 85 5 1 × 1 7 1 = 85 Through this we see that the LCM of 85 and 17 is 85. How to Find the LCM of 85 and 17 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 85 and 17 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, 85 and 17: What are the Multiples of 85? What are the Multiples of 17? Let’s take a look at the first 10 multiples for each of these numbers, 85 and 17: First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850 First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 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 85 and 17 are 85, 170, 255. Because 85 is the smallest, it is the least common multiple. The LCM of 85 and 17 is 85. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 50 and 126? What is the LCM of 133 and 115? What is the LCM of 93 and 100? What is the LCM of 136 and 122? What is the LCM of 103 and 3?