Question

How many numbers from 1 to 1000 are there which are not divisible by any of the digits 2, 3 and 5?

Answer 1

First we will take LCM of 2, 3 & 5 which is 30
then the next nos will be 60, 90, 120..... which are exactly divisible by 2, 3 & 5...
Clearly it forms an ap with first term = 30 and common difference = 30..
Last no between 1 to 1000 which is exactly divisible by given numbers is 990 .

Now
990 = a + (n - 1) d
= 990 = 30 + (n - 1) (30)
= 990-30/30 = (n - 1)
= 960/30 = n - 1
= 32 + 1 = n
= 33 = n

Hence there are 33 no lie between 1 to 1000 which are exactly divisible by 2, 3 and 5..

Hope it will be helpful..