Question

Find the number of numbers from 1 to 100 which are not divisible by any one of 2, 3, 5,

Answer 1

Numbers divisible by 2 = 50

Numbers divisible by 3 = 33

Numbers divisible by 5 = 20


Taking two numbers combined(2 × 3)

Numbers divisible by 6 (LCM of 2 & 3) = 16


Taking another two numbers combined(2 × 5)

Numbers divisible by 10 (LCM of 2 & 5) = 10


Taking the other(3 × 5)

Numbers divisible by 15 (LCM of 3 & 5) = 6


Now taking all the three(2 × 3 × 5)

Numbers divisible by 30 (LCM of 2, 3 & 5) = 3


Numbers divisible by 2, 3 & 5 combined
= 50 + 33 + 20 - (16 + 10 + 6) + 3 = 103 - 32 + 3 = 106 - 32 = 74


Numbers not divisible by 2, 3 & 5 = 100 - 74 = 26.

-WonderGirl