The multiples the **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 typical Multiple**of 3 and also 5 is **15**

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

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

We obtain a **multiple** the a number once we **multiply that by another number**. Such as multiplying by 1, 2, 3, 4, 5, etc, however not zero. Similar to 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: What are the first five multiples of 4 |

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

## What is a "Common Multiple" ?

Say we have detailed the first few multiples the **4** and **5**: the **common multiples** space those the are uncovered in both lists:

The multiples that 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 common multiples of 4 and 5 are: 20, 40,** (and **60**, **80**, and so on ..., too)

## What is the "Least usual Multiple" ?

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

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

... For this reason the **Least** typical Multiple the 4 and 5 is **20**.

## recognize the Least common Multiple

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

### Example: uncover the least common multiple of 4 and 10:

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

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

So the least common 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 complement at 30

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

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

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

Hint: We have the right to have smaller sized lists for the enlarge numbers.

## Least typical Multiple Tool

There is one more method: the Least common Multiple device does it automatically. (Yes, we waited till the end to phone call you!)

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