Find the prime factors of 28 A. 2, 4, 7 B. 2, 7 C. 4, 7 D. 1, 2, 4, 7 and 28

So, the prime factorization of 24 is $2 \times 2 \times 2 \times 3$, which can be written as $2^3 \times 3^1$.

For a number to be a perfect square, all the exponents in its prime factorization must be even. In $2^3 \times 3^1$, the exponent of 2 is 3 (odd) and the exponent of 3 is 1 (odd).

To make the exponent of 2 even, we need to multiply by $2^1$.
To make the exponent of 3 even, we need to multiply by $3^1$.
The smallest number to multiply 24 by is the product of these missing factors:

If we multiply 24 by 6, we get:

Since both exponents (4 and 2) are even, the resulting number is a perfect square.

And $144 = 12^2$, which is a perfect square.

Comparing this with the given options, the smallest number is 6.

The final answer is $\boxed{\text{A. 6}}$.