Project Euler: challenging mathematical/computer programming problems

I'm going through the first problem.

"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."

I've started going through it yesterday. It took me about an hour to find out all the multiples of 3, and it was fun to make it work out. Now figuring out a way to add them...