What is the smallest positive perfect square that is divisible by both 2 and 3?
I need to find a number that is both a perfect square and a multiple of 2 and 3. A perfect square means that the number can be written as the square of an integer, like 4 = 2^2 or 25 = 5^2. A multiple of 2 and 3 means that the number is even and divisible by 3, like 6 or 12. I can try some small perfect squares and see if they meet the other conditions. 1 = 1^2 is not even, so it is not a multiple of 2. 4 = 2^2 is even, but not divisible by 3, so it is not a multiple of 3. 9 = 3^2 is divisible by 3, but not even, so it is not a multiple of 2. 16 = 4^2 is even, but not divisible by 3, so it is not a multiple of 3. 25 = 5^2 is not even, so it is not a multiple of 2. 36 = 6^2 is both even and divisible by 3, so it is a multiple of 2 and 3. I have found the smallest positive perfect square that is divisible by both 2 and 3, and it is 36. 