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8 of the numbers less than 660 are divisible by 5 and 11 but not 3.

All numbers divisible by 5 and 11 are multiples of their lcm; lcm(5, 11) = 55

All numbers divisibile by 5, 11 and 3 are multiples of their lcm; lcm(5, 11, 3) = 165

659 ÷ 55 = 11 54/55 → 11 numbers less than 660 are divisible by 5 and 11

659 ÷ 165 = 3 164/165 → 3 numbers less than 660 are divisible by 5, 11 and 3

→ of the 11 numbers less than 660 divisible by 5 and 11, 3 are also divisible by 3

→ 11 - 3 = 8 numbers less than 660 are divisible by 5 and 11 but not 3,.

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2014-09-14 13:00:09
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Q: How many natural numbers below 660 are divisible by 5 and 11 but not by 3?
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