Solution: The LCM of 31 and 82 is 2542
Methods
How to find the LCM of 31 and 82 using Prime Factorization
One way to find the LCM of 31 and 82 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 82?
Here is the prime factorization of 31:
3
1
1
31^1
3 1 1
And this is the prime factorization of 82:
2
1
×
4
1
1
2^1 × 41^1
2 1 × 4 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: 31, 2, 41
2
1
×
3
1
1
×
4
1
1
=
2542
2^1 × 31^1 × 41^1 = 2542
2 1 × 3 1 1 × 4 1 1 = 2542
Through this we see that the LCM of 31 and 82 is 2542.
How to Find the LCM of 31 and 82 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 31 and 82 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 82:
What are the Multiples of 31?
What are the Multiples of 82?
Let’s take a look at the first 10 multiples for each of these numbers, 31 and 82:
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
First 10 Multiples of 82: 82, 164, 246, 328, 410, 492, 574, 656, 738, 820
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 82 are 2542, 5084, 7626. Because 2542 is the smallest, it is the least common multiple.
The LCM of 31 and 82 is 2542.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 61 and 119?
What is the LCM of 40 and 1?
What is the LCM of 47 and 92?
What is the LCM of 118 and 143?
What is the LCM of 103 and 114?