# Code Corner: Counting Multiples

### 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.

Source

#### 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.