Question

find the greatest 4-digit no. which is exactly divisible by each of 8,12 and 20

Answer 1

8 = 2^3
12 = 2^2*3
20 = 2^2*5
LCM = 2^3*3^5 = 120
Greatest 4 digit no. = 9999
Greatest 4 digit no. exactly divisible by 8, 12 and 20 = 9999 - the remainder of 9999/LCM

Remainder of 9999/120 = 39
9999-39 = 9960
The greatest 4 digit no. exactly divisible by 8, 12 and 20 is 9960


 

Answer 2

The greatest 4 digit no. exactly divisible by 8, 12 and 20 is 9960