Solution: The LCM of 65 and 70 is 910
Methods
How to find the LCM of 65 and 70 using Prime Factorization
One way to find the LCM of 65 and 70 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 70?
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 70:
2
1
×
5
1
×
7
1
2^1 × 5^1 × 7^1
2 1 × 5 1 × 7 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, 7
2
1
×
5
1
×
7
1
×
1
3
1
=
910
2^1 × 5^1 × 7^1 × 13^1 = 910
2 1 × 5 1 × 7 1 × 1 3 1 = 910
Through this we see that the LCM of 65 and 70 is 910.
How to Find the LCM of 65 and 70 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 65 and 70 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 70:
What are the Multiples of 65?
What are the Multiples of 70?
Let’s take a look at the first 10 multiples for each of these numbers, 65 and 70:
First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650
First 10 Multiples of 70: 70, 140, 210, 280, 350, 420, 490, 560, 630, 700
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 70 are 910, 1820, 2730. Because 910 is the smallest, it is the least common multiple.
The LCM of 65 and 70 is 910.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 100 and 48?
What is the LCM of 86 and 93?
What is the LCM of 131 and 83?
What is the LCM of 103 and 90?
What is the LCM of 62 and 133?