Q:

What is the LCM of 43 and 31?

Accepted Solution

A:
Solution: The LCM of 43 and 31 is 1333 Methods How to find the LCM of 43 and 31 using Prime Factorization One way to find the LCM of 43 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 43? What are the Factors of 31? Here is the prime factorization of 43: 4 3 1 43^1 4 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: 43, 31 3 1 1 × 4 3 1 = 1333 31^1 × 43^1 = 1333 3 1 1 × 4 3 1 = 1333 Through this we see that the LCM of 43 and 31 is 1333. How to Find the LCM of 43 and 31 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 43 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, 43 and 31: What are the Multiples of 43? What are the Multiples of 31? Let’s take a look at the first 10 multiples for each of these numbers, 43 and 31: First 10 Multiples of 43: 43, 86, 129, 172, 215, 258, 301, 344, 387, 430 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 43 and 31 are 1333, 2666, 3999. Because 1333 is the smallest, it is the least common multiple. The LCM of 43 and 31 is 1333. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 22 and 61? What is the LCM of 118 and 145? What is the LCM of 20 and 8? What is the LCM of 50 and 88? What is the LCM of 24 and 101?