# What is the LCM of 10 and 8?

The LCM, or Least Common Multiple, of two or more numbers is the smallest value that all the numbers considered can be divided into evenly. So, the LCM of 10 and 8 would be the smallest number that can be divided by both 10 and 8 exactly, without any remainder left afterwards.

## Solution: The LCM of 10 and 8 is 40

Methods

### How to find the LCM of 10 and 8 using Prime Factorization

One way to find the LCM of 10 and 8 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:

Here is the prime factorization of 10:

$2^1 × 5^1$

And this is the prime factorization of 8:

$2^3$

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, 5

$2^3 × 5^1 = 40$

Through this we see that the LCM of 10 and 8 is 40.

### How to Find the LCM of 10 and 8 by Listing Common Multiples

The first step to this method of finding the Least Common Multiple of 10 and 8 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, 10 and 8:

What are the Multiples of 10?

What are the Multiples of 8?

Let’s take a look at the first 10 multiples for each of these numbers, 10 and 8:

First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

First 10 Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

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 10 and 8 are 40, 80, 120. Because 40 is the smallest, it is the least common multiple.

The LCM of 10 and 8 is 40.

### Find the LCM of Other Number Pairs

Want more practice? Try some of these other LCM problems: #### 8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

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