Find the smallest number that should be added to 1500, so that the sum is exactly divisible by 18, 20 and 24.

The smallest number that is exactly divisible by18,20 and 24.we take their lowest common mutipleL.C.M. of 18, 20, 24 is 

2 x 2 x 2 x 3 x 3 x 5 =360Number just greater than1500 is divisible by 360 1500 / 360=Quotient = 4 Remainder = 60 Number which will be added 1500+ ( 360 - 60 ) 1500 + 300 = 1800 Required number is 300 when added to1500 will be exactly divisible by18,20,24 As we division is repeated subtraction (1)  1500 - 360 = 1140(2)  1140 - 360 = 780(3) 780 - 360 = 420(4) 420 - 360 = 60

To make last 5th set we will add 300 to 60 to bring 0 60 + 300 = 360(5) 360 - 360  = 0 

so number 300 which will be added to 1500