Q:

What is the LCM of 85 and 103?

Accepted Solution

A:
Solution: The LCM of 85 and 103 is 8755 Methods How to find the LCM of 85 and 103 using Prime Factorization One way to find the LCM of 85 and 103 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 103? 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 103: 10 3 1 103^1 10 3 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, 103 5 1 × 1 7 1 × 10 3 1 = 8755 5^1 × 17^1 × 103^1 = 8755 5 1 × 1 7 1 × 10 3 1 = 8755 Through this we see that the LCM of 85 and 103 is 8755. How to Find the LCM of 85 and 103 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 85 and 103 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 103: What are the Multiples of 85? What are the Multiples of 103? Let’s take a look at the first 10 multiples for each of these numbers, 85 and 103: First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850 First 10 Multiples of 103: 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030 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 103 are 8755, 17510, 26265. Because 8755 is the smallest, it is the least common multiple. The LCM of 85 and 103 is 8755. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 38 and 114? What is the LCM of 21 and 45? What is the LCM of 28 and 122? What is the LCM of 83 and 42? What is the LCM of 5 and 60?