Explanation:

First of all find the LCM of 15, 24 and 36

15 = 3 * 5

24 = 2^3 * 3

36 = 2^2 * 3*2

So Lcm will be the highest power of all these multiples = 2^3 *3^2 * 5 = 360

Now 15 , 24 and 36 will divide exactly all the multiples of 360.

So 15, 24 and 36 will exactly divide 360, 720,1080 and so on…..

So for finding the greatest 4 digit number find the number of complete multiples required by dividing the 5 digit smallest number by 360

10000/360 =27.77

Quotient = 27

The largest 4 digit exactly divisible by above numbers are :

360*27 = 9720

Hence, option 2 is the correct answer.