The multiples of **3** are 3, 6, 9, 12, 15, 18, ... etc**The multiples of 5** are 5, 10, 15, 20, 25, ... etc

Find the initially **Common** (same) value:

The **Leastern Common Multiple**of 3 and also 5 is **15**

(15 is a multiple of both 3 and 5, and is the smallest number like that.)

## So ... what is a "Multiple" ?

We get a **multiple** of a number when we **multiply it by an additional number**. Such as multiplying by 1, 2, 3, 4, 5, etc, however not zero. Just like the multiplication table. **Here are some examples: **

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,... You are watching: Least common multiple of 4 and 8 |

The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,... |

## What is a "Common Multiple" ?

Say we have actually detailed the initially few multiples of **4** and also **5**: the **prevalent multiples** are those that are found in both lists:

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,... |

The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,... |

Notice that **20** and **40** appear in both lists? **So, the common multiples of 4 and also 5 are: 20, 40,** (and **60**, **80**, etc ..., too)

## What is the "Leastern Common Multiple" ?

It is ssuggest the **smallest** of the prevalent multiples.

In our previous instance, the smallest of the widespread multiples is **20** ...

... so the **Least** Common Multiple of 4 and 5 is **20**.

## Finding the Leastern Usual Multiple

List the multiples of the numbers till we acquire our initially enhance.

### Example: Find the leastern common multiple of 4 and 10:

The multiples of 4 are: **4, 8, 12, 16, 20, ...****and also the multiples of 10 are: 10, 20, ...**

Aha! tright here is a enhance at 20. It looks favor this:

So the least common multiple of 4 and 10 is **20**

### Example: Find the least common multiple of 6 and also 15:

The multiples of 6 are: **6, 12, 18, 24, 30, ...****and also the multiples of 15 are: 15, 30, ...**

Tbelow is a enhance at 30

So the leastern widespread multiple of 6 and also 15 is **30**

### Example: Find the leastern common multiple of 4, 6, and 8

Multiples of 4 are: 4, 8, 12, 16, 20, **24**, 28, 32, 36, ...**Multiples of 6 are: 6, 12, 18, 24**, 30, 36, ...**Multiples of 8 are: 8, 16, 24**, 32, 40, ....

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So **24** is the leastern prevalent multiple (I can not discover a smaller one!)

Hint: We deserve to have actually smaller sized lists for the bigger numbers.

## Least Typical Multiple Tool

There is an additional method: the Leastern Typical Multiple Device does it automatically. (Yes, we waited until the end to tell you!)

Introduction to Fractions Simplifying Fractions Comparing Fractions Least Usual Multiple Tool Leastern Common Denominator Greatest Usual Factor Adding Fractions Subtracting Fractions Fractions Index