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# What is the sum of all the multiples of 3 and 5 below 500?

The sum of all multiples of 3 below 500 is the sum of 3 + 6 + ... + 498 = 41583

The sum of all multiples of 5 below 500 is the sum of 5 + 10 + ... + 495 = 24750

Depending upon the interpretation of "of 3 and 5", the answer is one of:

1. The sum of all multiples of both 3 and 5 below 500 is the sum of 15 + 30 + ... + 495 = 8415
2. The sum of all multiples of 3 below 500 and all multiples of 5 below 500 is 41583 + 24750 = 66333
3. Since the multiples of both 3 and 5 (that is 15, 30, ...) have been counted twice - once in the multiples of 3 and once in the multiples of 5 - the sum of all multiples of 3 or 5 or both below 500 is 41583 + 24750 - 8415 = 57918

I have emphasised the word below with regard to 500 since 500 is a multiple of 5, but 500 is not below (less than) itself, that is the multiples are of the numbers 1, 2, 3, ..., 499. If the question was intended to mean less than or equal to 500, add an extra 500 to the multiples of 5 above, making the sum of the multiples of 5 be 25250 and the final sums (1) 8415, (2) 66833, (3) 58418. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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