What is the smallest four-digit number that is divisible by 15, 25, 40, and 75?

Explanation

The least common multiple (LCM) of 15, 25, 40, and 75 is 600. The smallest four-digit number divisible by all these is the smallest four-digit multiple of 600. Since 600 × 16 = 9600, 9600 is the smallest four-digit number divisible by all given numbers.