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.
This is a simple problem. How do you generate a sequence of integers that are a) multiples of 3 and b) multiples of 5 less than 1000? Do these two sequences intersect each other? If so, how do you find these integers that are multiples of 3 and 5? Thinking along these lines should help you solve the problem easily.