Solution: The LCM of 65 and 135 is 1755
Methods
How to find the LCM of 65 and 135 using Prime Factorization
One way to find the LCM of 65 and 135 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 65?
What are the Factors of 135?
Here is the prime factorization of 65:
5
1
×
1
3
1
5^1 × 13^1
5 1 × 1 3 1
And this is the prime factorization of 135:
3
3
×
5
1
3^3 × 5^1
3 3 × 5 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: 5, 13, 3
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 65 and 135 is 1755.
How to Find the LCM of 65 and 135 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 65 and 135 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, 65 and 135:
What are the Multiples of 65?
What are the Multiples of 135?
Let’s take a look at the first 10 multiples for each of these numbers, 65 and 135:
First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650
First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350
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 65 and 135 are 1755, 3510, 5265. Because 1755 is the smallest, it is the least common multiple.
The LCM of 65 and 135 is 1755.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 59 and 142?
What is the LCM of 35 and 66?
What is the LCM of 64 and 63?
What is the LCM of 45 and 68?
What is the LCM of 126 and 108?