Question

How many numbers are there between 1 and 100 that are not divisible by 2,3 and 5?

• A. 26
• B. 36
• C. 40
• D. 68
• E. 48

Answer 1

The correct option is A

26

Numbers divisible by 2 = 50

Numbers divisible by 3 = 33

Numbers divisible by 5 = 20
Numbers divisible by 6 (LCM of 2 & 3) = 16
Numbers divisible by 10 (LCM of 2 & 5) = 10
Numbers divisible by 15 (LCM of 3 & 5) = 6
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