# How can you find the least common multiple using prime factorization?

##### 1 Answer

See process below:

#### Explanation:

Let's come up with a problem so that I can show you the process.

**What is the least common multiple of 12 and 9?**

Let's prime factor each of the numbers:

12's prime factors are

9's prime factors are

Now make a chart with both of the numbers:

This is where it gets a little tricky. What we're going to is find the lowest number in our prime factorization. That number is

Obviously, 12 has more 2's because 9 has none.

Now what's the other number in our prime factorization?

9 has more 3's than 12, so I am going to cross out the other 3. We only want the part with the most threes.

Put all of the highlighted numbers down into one multiplication problem:

**36** is the least common multiple between 12 and 9.

This is a really helpful video on YouTube about this topic:least common multiple