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 first **Common** (same) value:

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

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

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

We obtain a **multiple** that a number once 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 room some examples: **

The multiples that 4 are: 4,8,12,16,20,24,28,32,36,40,44,... You are watching: Lowest common multiple of 4 and 10 |

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

## What is a "Common Multiple" ?

Say us have listed the first few multiples of **4** and also **5**: the **common multiples** room those that are uncovered 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**, etc ..., too)

## What is the "Least usual Multiple" ?

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

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

... For this reason the **Least** usual Multiple that 4 and also 5 is **20**.

## finding the Least usual Multiple

List the multiples that the numbers until we gain our first match.

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

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

Aha! there is a complement at 20. That looks choose this:

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

### Example: discover the least typical multiple the 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 of 6 and also 15 is **30**

### Example: uncover the least common multiple that 4, 6, and also 8

Multiples that 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, ....

See more: How Far Is Birmingham Alabama To Atlanta Georgia, Atlanta To Birmingham Distance (Atl To Bhm)

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

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

## Least common Multiple Tool

There is another method: the Least usual Multiple tool does the automatically. (Yes, us waited until the finish to phone call you!)

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