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.