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2015-02-07T17:39:42+08:00

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The question, if I am right is in short, asking how many integers from 1 - 500 cannot be divided by both 5 and 3. That means, the least common multiple of 5 and 3 which is 15, and the rest of the multiples of 15 are out of the picture. So, what we do is, FIND THE NUMBER OF MULTIPLES OF 15 FROM 1- 500. In order to do that, we use this method: 

{ [(number closest to 500 that is a multiple of 15) - (number closest to 1 that is a multiple of 15) ] divided by 15 } + 1 subtracted from 500 = ANSWER

Let us translate this to symbols:
500 - [ \frac{495 - 15}{15} + 1 ]


  500 - [ \frac{480}{15} + 1 ]

500 -  [ 32 + 1 ]

500 - 33

ANSWER:
                467


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