Numbers Divisible by 15

Question

in a set of odd numbers less than 500, What is the total number of numbers divisible by 15?

Comments

See, numbers divisible by 15 are in order of 15, 30, 45, 60, so on. We are getting 1 odd then 1 even again odd and even, so on. Therefore we'll have to divide by 2 here.

For multiple of 7 : $\left \lfloor \frac{500}{7} \right \rfloor$ = 71

Odd numbers = $\left \lceil \frac{71}{2} \right \rceil$ = 36

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@Kantikumar

Actually I was asking the other way ,

" In a set of numbers which are multiple of 7 and less than 500 , What is the total number of numbers divisible by 15 "

Here we will divide 33 / 7  , right ?

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Nopes.

Here required number will be multiple of both 7 and 15.

$\therefore$LCM(7,15) = 105

Total numbers divisible by 105 = $\left \lfloor \frac{500}{105} \right \rfloor$ = 4

Total odd numbers = $\frac{4}{2}$ = 2.