Solution: The LCM of 42 and 65 is 2730
Methods
How to find the LCM of 42 and 65 using Prime Factorization
One way to find the LCM of 42 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 42?
What are the Factors of 65?
Here is the prime factorization of 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 1 × 7 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: 2, 3, 7, 5, 13
2
1
×
3
1
×
5
1
×
7
1
×
1
3
1
=
2730
2^1 × 3^1 × 5^1 × 7^1 × 13^1 = 2730
2 1 × 3 1 × 5 1 × 7 1 × 1 3 1 = 2730
Through this we see that the LCM of 42 and 65 is 2730.
How to Find the LCM of 42 and 65 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 42 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, 42 and 65:
What are the Multiples of 42?
What are the Multiples of 65?
Let’s take a look at the first 10 multiples for each of these numbers, 42 and 65:
First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420
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 42 and 65 are 2730, 5460, 8190. Because 2730 is the smallest, it is the least common multiple.
The LCM of 42 and 65 is 2730.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 130 and 86?
What is the LCM of 93 and 135?
What is the LCM of 108 and 129?
What is the LCM of 10 and 20?
What is the LCM of 56 and 90?