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

Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.

On dividing 9999 by 600, the remainder is 399.

 Required number (9999 - 399) = 9600.