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

Find the an initial **Common** (same) value:

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

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

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

We gain a **multiple** of a number when we **multiply that by an additional number**. Such together multiplying through 1, 2, 3, 4, 5, etc, however not zero. As with the multiplication table. **Here space some examples: **

The multiples the 4 are: 4,8,12,16,20,24,28,32,36,40,44,... You are watching: Common multiples of 5 and 10 |

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

## What is a "Common Multiple" ?

Say we have detailed the first couple of multiples the **4** and also **5**: the **common multiples** space those the are found 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 also **40** appear in both lists? **So, the usual multiples that 4 and 5 are: 20, 40,** (and **60**, **80**, and so on ..., too)

## What is the "Least common Multiple" ?

It is merely the **smallest** that the common multiples.

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

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

## recognize the Least typical Multiple

List the multiples the the numbers until we acquire our first match.

### Example: find the least usual multiple that 4 and also 10:

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

Aha! over there is a enhance at 20. It looks favor this:

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

### Example: discover the least typical multiple of 6 and 15:

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

There is a enhance at 30

So the least common multiple the 6 and also 15 is **30**

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

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

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

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

## Least typical Multiple Tool

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

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