Solution: The LCM of 31 and 58 is 1798
Methods
How to find the LCM of 31 and 58 using Prime Factorization
One way to find the LCM of 31 and 58 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 31?
What are the Factors of 58?
Here is the prime factorization of 31:
3
1
1
31^1
3 1 1
And this is the prime factorization of 58:
2
1
×
2
9
1
2^1 × 29^1
2 1 × 2 9 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: 31, 2, 29
2
1
×
2
9
1
×
3
1
1
=
1798
2^1 × 29^1 × 31^1 = 1798
2 1 × 2 9 1 × 3 1 1 = 1798
Through this we see that the LCM of 31 and 58 is 1798.
How to Find the LCM of 31 and 58 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 31 and 58 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, 31 and 58:
What are the Multiples of 31?
What are the Multiples of 58?
Let’s take a look at the first 10 multiples for each of these numbers, 31 and 58:
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
First 10 Multiples of 58: 58, 116, 174, 232, 290, 348, 406, 464, 522, 580
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 31 and 58 are 1798, 3596, 5394. Because 1798 is the smallest, it is the least common multiple.
The LCM of 31 and 58 is 1798.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 56 and 75?
What is the LCM of 17 and 73?
What is the LCM of 69 and 6?
What is the LCM of 66 and 140?
What is the LCM of 64 and 72?