Solution: The LCM of 65 and 36 is 2340
Methods
How to find the LCM of 65 and 36 using Prime Factorization
One way to find the LCM of 65 and 36 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 36?
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 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
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, 2, 3
2
2
×
3
2
×
5
1
×
1
3
1
=
2340
2^2 × 3^2 × 5^1 × 13^1 = 2340
2 2 × 3 2 × 5 1 × 1 3 1 = 2340
Through this we see that the LCM of 65 and 36 is 2340.
How to Find the LCM of 65 and 36 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 65 and 36 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 36:
What are the Multiples of 65?
What are the Multiples of 36?
Let’s take a look at the first 10 multiples for each of these numbers, 65 and 36:
First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650
First 10 Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360
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 36 are 2340, 4680, 7020. Because 2340 is the smallest, it is the least common multiple.
The LCM of 65 and 36 is 2340.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 142 and 122?
What is the LCM of 45 and 76?
What is the LCM of 8 and 41?
What is the LCM of 113 and 79?
What is the LCM of 24 and 103?