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How many of the first 500 positive integers are divisible by 3, 4 and 5?

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How many of the first 500 positive integers are divisible by 3, 4 and 5?

Firewolf  Jun 17, 2018
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The least common multiple of 3,4, and 5 is the smallest integer that is also divisible by 3,4, and 5. Because 3,4, and 5 do not share any common factors, the least common multiple can be determined by finding the product of 3,4, and 5.

$$3*4*5=60$$

All multiples of 60 bounded between 1 and 500 are the only integers that satisfy the original condition. $$500/60$$ or $$8.\overline{3}$$ represents the number of multiples of 60. Of course, multiples can only be counted as whole numbers, so there are only 8 integers that are divisible by 3,4, and 5.

TheXSquaredFactor  Jun 17, 2018
edited by TheXSquaredFactor  Jun 17, 2018