Solution: The LCM of 135 and 39 is 1755
Methods
How to find the LCM of 135 and 39 using Prime Factorization
One way to find the LCM of 135 and 39 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 135?
What are the Factors of 39?
Here is the prime factorization of 135:
3
3
×
5
1
3^3 × 5^1
3 3 × 5 1
And this is the prime factorization of 39:
3
1
×
1
3
1
3^1 × 13^1
3 1 × 1 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, 5, 13
3
3
×
5
1
×
1
3
1
=
1755
3^3 × 5^1 × 13^1 = 1755
3 3 × 5 1 × 1 3 1 = 1755
Through this we see that the LCM of 135 and 39 is 1755.
How to Find the LCM of 135 and 39 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 135 and 39 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, 135 and 39:
What are the Multiples of 135?
What are the Multiples of 39?
Let’s take a look at the first 10 multiples for each of these numbers, 135 and 39:
First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350
First 10 Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390
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 135 and 39 are 1755, 3510, 5265. Because 1755 is the smallest, it is the least common multiple.
The LCM of 135 and 39 is 1755.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 117 and 121?
What is the LCM of 105 and 20?
What is the LCM of 50 and 28?
What is the LCM of 32 and 93?
What is the LCM of 1 and 71?