How many numbers less than 10000 are there which are exactly divisible by 21 , 35 and 63 ?

Correct option is D

To Find:

Numbers less than 10000 are there which are exactly divisible by 21, 35 and 63.

Solution:

​$$21 = 3\times7 \\35 = 5\times 7\\63= 3^2\times 7$$

LCM(21, 35, 63) = 315

The number less than 10000 which is divisible by 315 are given by $$\frac{10000}{315}$$ i.e integral part when 10000 is divided by 315 is 31.

Therefore, there are 31 numbers less than 10000 which are exactly divisible by 21, 35 and 63.