Solution: The LCM of 12 and 82 is 492
Methods
How to find the LCM of 12 and 82 using Prime Factorization
One way to find the LCM of 12 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 12?
What are the Factors of 82?
Here is the prime factorization of 12:
2
2
×
3
1
2^2 × 3^1
2 2 × 3 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: 2, 3, 41
2
2
×
3
1
×
4
1
1
=
492
2^2 × 3^1 × 41^1 = 492
2 2 × 3 1 × 4 1 1 = 492
Through this we see that the LCM of 12 and 82 is 492.
How to Find the LCM of 12 and 82 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 12 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, 12 and 82:
What are the Multiples of 12?
What are the Multiples of 82?
Let’s take a look at the first 10 multiples for each of these numbers, 12 and 82:
First 10 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
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 12 and 82 are 492, 984, 1476. Because 492 is the smallest, it is the least common multiple.
The LCM of 12 and 82 is 492.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 133 and 142?
What is the LCM of 103 and 26?
What is the LCM of 147 and 19?
What is the LCM of 48 and 57?
What is the LCM of 116 and 65?