Solution: The LCM of 83 and 32 is 2656
Methods
How to find the LCM of 83 and 32 using Prime Factorization
One way to find the LCM of 83 and 32 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 83?
What are the Factors of 32?
Here is the prime factorization of 83:
8
3
1
83^1
8 3 1
And this is the prime factorization of 32:
2
5
2^5
2 5
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: 83, 2
2
5
×
8
3
1
=
2656
2^5 × 83^1 = 2656
2 5 × 8 3 1 = 2656
Through this we see that the LCM of 83 and 32 is 2656.
How to Find the LCM of 83 and 32 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 83 and 32 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, 83 and 32:
What are the Multiples of 83?
What are the Multiples of 32?
Let’s take a look at the first 10 multiples for each of these numbers, 83 and 32:
First 10 Multiples of 83: 83, 166, 249, 332, 415, 498, 581, 664, 747, 830
First 10 Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320
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 83 and 32 are 2656, 5312, 7968. Because 2656 is the smallest, it is the least common multiple.
The LCM of 83 and 32 is 2656.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 48 and 8?
What is the LCM of 67 and 118?
What is the LCM of 84 and 71?
What is the LCM of 140 and 25?
What is the LCM of 115 and 88?