Solution: The LCM of 65 and 88 is 5720
Methods
How to find the LCM of 65 and 88 using Prime Factorization
One way to find the LCM of 65 and 88 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 88?
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 88:
2
3
×
1
1
1
2^3 × 11^1
2 3 × 1 1 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, 2, 11
2
3
×
5
1
×
1
1
1
×
1
3
1
=
5720
2^3 × 5^1 × 11^1 × 13^1 = 5720
2 3 × 5 1 × 1 1 1 × 1 3 1 = 5720
Through this we see that the LCM of 65 and 88 is 5720.
How to Find the LCM of 65 and 88 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 65 and 88 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 88:
What are the Multiples of 65?
What are the Multiples of 88?
Let’s take a look at the first 10 multiples for each of these numbers, 65 and 88:
First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650
First 10 Multiples of 88: 88, 176, 264, 352, 440, 528, 616, 704, 792, 880
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 88 are 5720, 11440, 17160. Because 5720 is the smallest, it is the least common multiple.
The LCM of 65 and 88 is 5720.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 123 and 130?
What is the LCM of 41 and 99?
What is the LCM of 116 and 89?
What is the LCM of 91 and 102?
What is the LCM of 87 and 92?