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Multiple sums

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.

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If you enjoyed this puzzle, check out Sunday Afternoon Maths IX,
puzzles about numbers, or a random puzzle.

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