# What is the Lowest Common Multiple (LCM) of two numbers that don't have any common factors?

Jan 25, 2018

It is the product of the two numbers.

#### Explanation:

The way to find the LCM is to write out both factorizations of the numbers, and then combine any factors that the two numbers share.

So, if two numbers don't share any factors greater than one, you won't combine anything, and so the LCM will just be all of the factors of the two numbers multiplied together.

Let's do an example so you can see what I mean:

Find the LCM of 7 and 15

The factorization of 7 is $7$. The factorization of 15 is $3 \times 5$.

Since none of these factors are the same, there is nothing to combine.

Therefore, the LCM is $3 \times 5 \times 7 = 105$

Jan 25, 2018

When there is no common factor for the given numbers, LCM is the product of the given numbers.

#### Explanation:

When there is no common factor for the given numbers, LCM is the product of the given numbers.

eg.

1. LCM for 3,4 is 12

2. LCM for 7, 13, 15 = 7 * 13 * 15 = 1365

3. LCM of 2, 3, 4 = 12 as 2 is a factor of 4 but 4 & 3 are relative prime and hence the answer.