### Question

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

### Solution

The multiples of 3 are 3,6,9,12,15,18,21,24,27,30,….

The multiples of 5 are 5,10,15,20,25,30,35,40,45,….

The intersection of these two sequences is 15,30,45,…