Q:

What is the LCM of 85 and 88?

Accepted Solution

A:
Solution: The LCM of 85 and 88 is 7480 Methods How to find the LCM of 85 and 88 using Prime Factorization One way to find the LCM of 85 and 88 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 88? 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 88: 2 3 × 1 1 1 2^3 × 11^1 2 3 × 1 1 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, 2, 11 2 3 × 5 1 × 1 1 1 × 1 7 1 = 7480 2^3 × 5^1 × 11^1 × 17^1 = 7480 2 3 × 5 1 × 1 1 1 × 1 7 1 = 7480 Through this we see that the LCM of 85 and 88 is 7480. How to Find the LCM of 85 and 88 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 85 and 88 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 88: What are the Multiples of 85? What are the Multiples of 88? Let’s take a look at the first 10 multiples for each of these numbers, 85 and 88: First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850 First 10 Multiples of 88: 88, 176, 264, 352, 440, 528, 616, 704, 792, 880 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 88 are 7480, 14960, 22440. Because 7480 is the smallest, it is the least common multiple. The LCM of 85 and 88 is 7480. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 93 and 48? What is the LCM of 60 and 37? What is the LCM of 103 and 68? What is the LCM of 136 and 133? What is the LCM of 73 and 80?