Solution: The LCM of 43 and 82 is 3526
Methods
How to find the LCM of 43 and 82 using Prime Factorization
One way to find the LCM of 43 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 43?
What are the Factors of 82?
Here is the prime factorization of 43:
4
3
1
43^1
4 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: 43, 2, 41
2
1
×
4
1
1
×
4
3
1
=
3526
2^1 × 41^1 × 43^1 = 3526
2 1 × 4 1 1 × 4 3 1 = 3526
Through this we see that the LCM of 43 and 82 is 3526.
How to Find the LCM of 43 and 82 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 43 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, 43 and 82:
What are the Multiples of 43?
What are the Multiples of 82?
Let’s take a look at the first 10 multiples for each of these numbers, 43 and 82:
First 10 Multiples of 43: 43, 86, 129, 172, 215, 258, 301, 344, 387, 430
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 43 and 82 are 3526, 7052, 10578. Because 3526 is the smallest, it is the least common multiple.
The LCM of 43 and 82 is 3526.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 12 and 2?
What is the LCM of 142 and 72?
What is the LCM of 102 and 140?
What is the LCM of 117 and 9?
What is the LCM of 107 and 25?