What is the smallest five-digit number that is divisible by 12, 15, and 18 without any remainder?

Explanation

To find the smallest five-digit number divisible by 12, 15, and 18, first determine their least common multiple (LCM). The LCM of 12, 15, and 18 is 180. The smallest five-digit number is 10000. Dividing 10000 by 180 gives a quotient of 55 with a remainder. Multiplying 180 by 56 equals 10080, which is the smallest five-digit number divisible by all three. Therefore, the correct answer is 10080.