### Problem

We are given 3 numbers, a starting number **A**, an ending number **B** and an integer **K**, find the number of multiples of **K** there is between **A** and **B** inclusive.

#### Example

a = 6 b = 9 k = 2 Should return 2

### My solution

The ranges are irrelevant because this is a maths problem and thus regardless of whatever we enter we will always solve this in constant time. The formula we use is the one to calculate the **n-th** term for the sequence of multiples of **k **starting at the first multiple greater than or equal to **a**. This looks like:

an = a1 + (n - 1)k.(I can explain this equation if anyone is interested.)

Where

`an`

is the nth multiple`a1`

is the starting multiple`n`

is the number of multiples

We can solve for n to get `n = ( (an - a1) / k) + 1)`

We can then calculate our other variables as

```
an = Math.floor(b / k) * k
a1 = Math.ceil(a / k) * k
```

Code language: JavaScript (javascript)

And put everything together to get

```
function solution(a, b, k) {
const a1 = Math.ceil(a / k) * k
const an = Math.floor(b / k) * k
return ((an - a1) / k) + 1
}
```

Code language: JavaScript (javascript)

And that’s it.

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