Solution: The LCM of 7 and 10 is 70
Methods
How to find the LCM of 7 and 10 using Prime Factorization
One way to find the LCM of 7 and 10 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 7?
What are the Factors of 10?
Here is the prime factorization of 7:
7
1
7^1
7 1
And this is the prime factorization of 10:
2
1
×
5
1
2^1 × 5^1
2 1 × 5 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: 7, 2, 5
2
1
×
5
1
×
7
1
=
70
2^1 × 5^1 × 7^1 = 70
2 1 × 5 1 × 7 1 = 70
Through this we see that the LCM of 7 and 10 is 70.
How to Find the LCM of 7 and 10 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 7 and 10 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, 7 and 10:
What are the Multiples of 7?
What are the Multiples of 10?
Let’s take a look at the first 10 multiples for each of these numbers, 7 and 10:
First 10 Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
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 7 and 10 are 70, 140, 210. Because 70 is the smallest, it is the least common multiple.
The LCM of 7 and 10 is 70.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 63 and 103?
What is the LCM of 123 and 52?
What is the LCM of 46 and 37?
What is the LCM of 113 and 42?
What is the LCM of 6 and 111?