Question

How many numbers between 400 and 500 are exactly divisible by 12,15 and 20 ?
a) One
b) Two
c) Three
c) None of these

Answer 1

two numbers are divisible between 400 and 500

Answer 2

LCM of 12 15 and 20 can be computed by factorisation

12 = 3 * 2 * 2

15 =3 * 5

20 = 5 * 2 * 2

LCM = 3 * 2*2* 5 (highest power of each prime in each number)

= 60

so the number is divisible by 60

now 2 multiples of 60 *60*7 and 60*8 are between 400 and 500 so number of numbers = 2