Find the LCM of the numbers (the least number which all the given numbers divide) -

Prime factorization of numbers -

15 = 3 × 5

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

LCM of given numbers = product of prime factors with highest powers = 2³ × 3² × 5 = 360

We know that greatest four - digit number is 9999.

So, the greatest value closest to 9999 which 360 can divide can be find by Euclid’s division lemma -

Putting the values in the equation a = bq + r -

9999 = 360(27) + 279

So, highest four - digit number 360 can completely divide = 9999 - remainder = 9999 - 279 = 9270.