Q:

What is the LCM of 115 and 31?

Accepted Solution

A:
Solution: The LCM of 115 and 31 is 3565 Methods How to find the LCM of 115 and 31 using Prime Factorization One way to find the LCM of 115 and 31 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 115? What are the Factors of 31? Here is the prime factorization of 115: 5 1 × 2 3 1 5^1 × 23^1 5 1 × 2 3 1 And this is the prime factorization of 31: 3 1 1 31^1 3 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, 23, 31 5 1 × 2 3 1 × 3 1 1 = 3565 5^1 × 23^1 × 31^1 = 3565 5 1 × 2 3 1 × 3 1 1 = 3565 Through this we see that the LCM of 115 and 31 is 3565. How to Find the LCM of 115 and 31 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 115 and 31 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, 115 and 31: What are the Multiples of 115? What are the Multiples of 31? Let’s take a look at the first 10 multiples for each of these numbers, 115 and 31: First 10 Multiples of 115: 115, 230, 345, 460, 575, 690, 805, 920, 1035, 1150 First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310 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 115 and 31 are 3565, 7130, 10695. Because 3565 is the smallest, it is the least common multiple. The LCM of 115 and 31 is 3565. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 90 and 127? What is the LCM of 48 and 44? What is the LCM of 94 and 105? What is the LCM of 142 and 99? What is the LCM of 138 and 28?