### Instruction: What is the smallest positive perfect square that is divisible by both 2 and 3?### Response: 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.