Answer:

Using prime factorization:

15 = 3 × 5

24 = 2³ × 3

36 = 2² × 3²

LCM = 2³ × 3²× 5

LCM = 360

The greatest four-digit number is 9999.

Divide 9999 by 360,

279 – remainder

9999 – 279 = 9720 is exactly divisible by 360.

The greatest number of four digits which is exactly divisible by 15, 24 and 36 is 9720.