The greatest four digit number =9999we can get the required number by following steps:step 1 : Divide 9999 by LCM of 15,24 and 36 Step 2 : Subtract result of step 1 from 9999.Prime factorization :15=3×524=23×336=22×32LCM (15,24,36)= 23×32×5=360Step 1 :  Dividing 9999 by 360, we get 279 as remainder.Step 2 : subtract 279 from 99999999−279=9720 the greatest number of four digit which is exactly divisible by 15,24 and 36 is 9720.