# How to Get the Least Common Multiple of Numbers

In mathematics, a multiple is a product of any number and an integer. The numbers 16, -48 and 72 are multiples of 8 because 8 x 2 = 16, 8 x -3 = -48 and 8 x 9 = 72. Similarly, the first five positive multiples of 7 are the following:

**7, 14, 21, 28, 35**.

In this post, we will particularly talk about positive integers and positive multiples. This is in preparation for the discussions on addition and subtraction of fractions.

We can always find a common multiple given two or more numbers. For example, if we list all the positive multiples of 2 and 3, we have

2, 4, **6**, 8, 10, **12**, 14, 16, **18**, 20

and

3, **6**, 9, **12**, 15, **18**, 21, 24, 27, 30.

As we can see, in the list, 6, 12 and 18 are common multiples of 2 and 3. If we continue further, there are still other multiples, and in fact, we will never run out of multiples.

Can you predict the next five multiples of 2 and 3 without listing?

The most important among the multiples is the **least common multiple**. The least common multiple is the smallest among all the multiples. Clearly, the least common multiple of 2 and 3 is 6. Here are some examples.

* Example 1: *Find the least common multiple of 3 and 5

Multiples of 3: 3, 6, 9. 12, **15,** 18

Multiples of 5: 5, 10, **15**, 20, 25,30

As we can see, **15 **appeared as the first common multiple, so 15 is the least common multiple of 3 and 5.

* Example 2: *Find the least common multiple of 3, 4, and 6.

In this example, we find the least multiple that are common to the three numbers.

Multiples of 3: 3, 6, 9, **12**, 15

Multiples of 4: 4, 8, **12**, 16, 20

Multiples of 6: 6, **12**, 18, 24, 30

So, the least common multiple of 3, 4, and 6 is **12**.

** Example 3:** Find the least common multiple of 3, 8 and 12.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, **24**

Multiples of 8: 8, 16, **24**,

Mulitples of 12: 12, **24**, 36, 48, 60

So, the least common multiple of 3, 4 and 6 is **24**.

In the next part of this **series**, we will discuss about How to Add Fractions.

8x-3=-24 not -48.