Q:

What is the LCM of 133 and 31?

Accepted Solution

A:
Solution: The LCM of 133 and 31 is 4123 Methods How to find the LCM of 133 and 31 using Prime Factorization One way to find the LCM of 133 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 133? What are the Factors of 31? Here is the prime factorization of 133: 7 1 × 1 9 1 7^1 × 19^1 7 1 × 1 9 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: 7, 19, 31 7 1 × 1 9 1 × 3 1 1 = 4123 7^1 × 19^1 × 31^1 = 4123 7 1 × 1 9 1 × 3 1 1 = 4123 Through this we see that the LCM of 133 and 31 is 4123. How to Find the LCM of 133 and 31 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 133 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, 133 and 31: What are the Multiples of 133? What are the Multiples of 31? Let’s take a look at the first 10 multiples for each of these numbers, 133 and 31: First 10 Multiples of 133: 133, 266, 399, 532, 665, 798, 931, 1064, 1197, 1330 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 133 and 31 are 4123, 8246, 12369. Because 4123 is the smallest, it is the least common multiple. The LCM of 133 and 31 is 4123. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 85 and 29? What is the LCM of 66 and 64? What is the LCM of 33 and 42? What is the LCM of 128 and 47? What is the LCM of 102 and 107?