# What's the Lowest Common Multiple (LCM) of 12 and 15?

##### 4 Answers

#### Explanation:

When we're looking at the LCM (Least Common Multiple), we're looking for a number that both 12 and 15 are a factor of. Oftentimes people simply assume that if we multiply the two together, we'll find it. In this case, it'd be

I start with a prime factorization of both numbers:

To find the LCM, we want to have all the prime factors from both numbers accounted for.

For instance, there are two 2s (in the 12). Let's put those in:

There is one 3 in both the 12 and the 15, so we need one 3:

And there is one 5 (in the 15) so let's put that in:

#### Explanation:

another approach is to use teh relation

now

The LCM is

#### Explanation:

The LCM is the least common multiple. We can find the LCM by listing the multiples of the two numbers and identifying the lowest multiple they have in common.

The LCM is

#### Explanation:

Let's try to find the LCM of

We get:

We see that they both share

We divide each number by their LCM.

We multiply these two quotients and the LCM to get our final answer:

That is our answer!