Multiplicative Magic Square/Examples

Examples of Multiplicative Magic Squares

Order $1$

The Order $1$ multiplicative magic square is trivial:

$\begin{array}{|c|}

\hline 1 \\ \hline \end{array}$

Order $3$

Order $3$ Multiplicative Magic Square with Smallest Magic Constant

The order $3$ multiplicative magic square with the smallest magic constant is as follows:

$\begin{array}{|c|c|c|}

\hline 18 & 1 & 12 \\ \hline 4 & 6 & 9 \\ \hline 3 & 36 & 2 \\ \hline \end{array}$

Its magic constant is $216$.

Order $4$

Order $4$ Magic Square with Smallest Magic Constant

The order $4$ multiplicative magic square with the smallest magic constant is as follows:

$\begin{array}{|c|c|c|c|}

\hline 1 & 15 & 24 & 14 \\ \hline 12 & 28 & 3 & 5 \\ \hline 21 & 6 & 10 & 4 \\ \hline 20 & 2 & 7 & 18 \\ \hline \end{array}$

Its magic constant is $5040$.