Find the smallest three-digit number that is exactly divisible by 12, 15 and 24.

​We need to find the smallest three-digit number that is divisible by 12, 15, and 24.

To find a number that is divisible by multiple numbers, we calculate the LCM (Least Common Multiple) of those numbers. The smallest three-digit number divisible by 12, 15, and 24 will be the smallest multiple of their LCM that is a three-digit number.

​Solution:

​$$LCM(12, 15, 24) = 2^3 \times 3 \times 5 = 120$$​​