As perfect as a square! 3

We know that $A = 2^{x} \times 3^{y}$ . From the given information, we can deduce that

• $x - 1$ and $y$ must be even

• $x$ and $y-1$ must be a multiple of 3

The smallest value of $x$ which satisfy the above criteria is $3$ . Similarly, the smallest value of $y$ which satisfy the above criteria is $4$ .

Therefore, $A$ must be $2^{3} \times 3^{4} = 648$ .