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

Find the very first **Common** (same) value:

The **Least common Multiple**of 3 and also 5 is **15**

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

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

We obtain a **multiple** of a number as soon as we **multiply that by an additional number**. Such as multiplying by 1, 2, 3, 4, 5, etc, yet not zero. As with the multiplication table. **Here are some examples: **

The multiples that 4 are: 4,8,12,16,20,24,28,32,36,40,44,... You are watching: Multiples of 5 up to 100 |

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

## What is a "Common Multiple" ?

Say we have provided the first couple of multiples that **4** and also **5**: the **common multiples** space those that are discovered in both lists:

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

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

Notice the **20** and **40** appear in both lists? **So, the usual multiples of 4 and 5 are: 20, 40,** (and **60**, **80**, and so on ..., too)

## What is the "Least usual Multiple" ?

It is simply the **smallest** of the typical multiples.

In our previous example, the the smallest of the typical multiples is **20** ...

... Therefore the **Least** typical Multiple that 4 and also 5 is **20**.

## finding the Least usual Multiple

List the multiples of the numbers till we gain our an initial match.

### Example: find the least typical multiple that 4 and 10:

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

Aha! over there is a match at 20. The looks like this:

So the least typical multiple the 4 and also 10 is **20**

### Example: uncover the least common multiple that 6 and also 15:

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

There is a complement at 30

So the least typical multiple that 6 and 15 is **30**

### Example: discover the least common multiple of 4, 6, and 8

Multiples that 4 are: 4, 8, 12, 16, 20, **24**, 28, 32, 36, ...**Multiples that 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 least common multiple (I can"t uncover a smaller one!)

Hint: We deserve to have smaller lists because that the larger numbers.

## Least common Multiple Tool

There is another method: the Least common Multiple device does that automatically. (Yes, us waited till the end to phone call you!)

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