Solution: The LCM of 39 and 83 is 3237
Methods
How to find the LCM of 39 and 83 using Prime Factorization
One way to find the LCM of 39 and 83 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 39?
What are the Factors of 83?
Here is the prime factorization of 39:
3
1
×
1
3
1
3^1 × 13^1
3 1 × 1 3 1
And this is the prime factorization of 83:
8
3
1
83^1
8 3 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: 3, 13, 83
3
1
×
1
3
1
×
8
3
1
=
3237
3^1 × 13^1 × 83^1 = 3237
3 1 × 1 3 1 × 8 3 1 = 3237
Through this we see that the LCM of 39 and 83 is 3237.
How to Find the LCM of 39 and 83 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 39 and 83 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, 39 and 83:
What are the Multiples of 39?
What are the Multiples of 83?
Let’s take a look at the first 10 multiples for each of these numbers, 39 and 83:
First 10 Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390
First 10 Multiples of 83: 83, 166, 249, 332, 415, 498, 581, 664, 747, 830
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 39 and 83 are 3237, 6474, 9711. Because 3237 is the smallest, it is the least common multiple.
The LCM of 39 and 83 is 3237.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 20 and 138?
What is the LCM of 120 and 139?
What is the LCM of 75 and 101?
What is the LCM of 90 and 135?
What is the LCM of 82 and 43?