How many intergers between 1 and 500 inclusive are divisible by both 6 and 9 but not 4

Question

Mathematics

Diana Merritt

9 January, 01:11

How many intergers between 1 and 500 inclusive are divisible by both 6 and 9 but not 4

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Answers (1)

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Carina Pena · Answer 1

I think the answer is 14.

the smallest common multiple of 6 and 9 is 18. all multiples of 18 is divisible by 6 and 9.

500 : 18=27.777777777

there are 27 numbers between 1 and 500 that are divisible by both 6 and 9, but when the quotient is an even number, the multiple of 18 is divisible by 4 as well, so only the multiples of 18 that produce an odd quotient satisfy the requirement.

from 1 to 27, there are 14 odd numbers.