Solution: The LCM of 23 and 65 is 1495
Methods
How to find the LCM of 23 and 65 using Prime Factorization
One way to find the LCM of 23 and 65 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 23?
What are the Factors of 65?
Here is the prime factorization of 23:
2
3
1
23^1
2 3 1
And this is the prime factorization of 65:
5
1
×
1
3
1
5^1 × 13^1
5 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: 23, 5, 13
5
1
×
1
3
1
×
2
3
1
=
1495
5^1 × 13^1 × 23^1 = 1495
5 1 × 1 3 1 × 2 3 1 = 1495
Through this we see that the LCM of 23 and 65 is 1495.
How to Find the LCM of 23 and 65 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 23 and 65 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, 23 and 65:
What are the Multiples of 23?
What are the Multiples of 65?
Let’s take a look at the first 10 multiples for each of these numbers, 23 and 65:
First 10 Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230
First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650
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 23 and 65 are 1495, 2990, 4485. Because 1495 is the smallest, it is the least common multiple.
The LCM of 23 and 65 is 1495.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 42 and 113?
What is the LCM of 125 and 140?
What is the LCM of 118 and 50?
What is the LCM of 126 and 131?
What is the LCM of 103 and 134?