2023 Cayley Problem 13

The integer 2023 is equal to 7 \times 17^2. Which of the following is the smallest positive perfect square that is a multiple of 2023?

\textbf{(A)}\ 2023^2\quad \textbf{(B)}\ 4 \times 2023\quad \textbf{(C)}\ 7 \times 2023\quad \textbf{(D)}\ 17 \times 2023\quad \textbf{(E)}\ 7 \times 17 \times 2023

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.