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

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

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

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

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

We gain a **multiple** of a number as soon as we **multiply the by one more number**. Such together multiplying through 1, 2, 3, 4, 5, etc, however not zero. As with the multiplication table. **Here room some examples: **

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,... You are watching: What are common multiples of 4 and 6 |

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

## What is a "Common Multiple" ?

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

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

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

Notice that **20** and also **40** show up in both lists? **So, the typical multiples of 4 and also 5 are: 20, 40,** (and **60**, **80**, and so on ..., too)

## What is the "Least typical Multiple" ?

It is simply the **smallest** that the usual multiples.

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

... So the **Least** usual Multiple of 4 and 5 is **20**.

## finding the Least usual Multiple

List the multiples the the numbers till we acquire our very first match.

### Example: uncover the least common multiple that 4 and also 10:

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

Aha! over there is a match at 20. That looks favor this:

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

### Example: uncover the least usual multiple that 6 and 15:

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

There is a match at 30

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

### Example: uncover the least usual multiple that 4, 6, and also 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 that 8 are: 8, 16, 24**, 32, 40, ....

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So **24** is the least common multiple (I can"t find a smaller one!)

Hint: We have the right to have smaller lists because that the bigger numbers.

## Least usual Multiple Tool

There is an additional method: the Least common Multiple device does the automatically. (Yes, us waited until the finish to call you!)

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