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

Explanation

First find the LCM. 15 = 3×5, 25 = 5^2, 40 = 2^3×5, and 75 = 3×5^2. Therefore, LCM = 2^3×3×5^2 = 600. The largest four-digit multiple of 600 is 600×16 = 9600. Since 600×17 = 10200, which has five digits, 9600 is the greatest four-digit multiple.