The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: _____

Greatest number of 4-digits is 9999.

To find the LCM of 15, 25, 40 and 75.

15 = 3 × 5

25 = 5 × 5

40 = 2 × 2 × 2 × 5

75 = 3 × 5 × 5

L.C.M. of 15, 25, 40 and 75 = 2 × 2 × 2 × 3 × 5 × 5 = 600.

On dividing 9999 by 600, the remainder is 399.

Required number (9999 - 399) = 9600.