KöMaL 2018 C1504

A $3\times3$ table is filled in as shown. If the greatest common divisor of any set of $n$ entries of the table is $n$, it is allowed to rearrange those entries so that none of them stay in place. With an appropriate succession of such steps, is it possible to achieve that the final arrangement of the numbers is a reflection of the original arrangement in one diagonal? In the other diagonal? 1 3 4 6 8 9 10 12 20