Ratio of Number to Reversal which is Multiple

Theoren
Take a (strictly) positive integer $n$, written in conventional decimal notation.

Let $m$ be the reversal of $n$.

Let $m = k n$ where $k$ is an integer.

Then $k$ is either $4$ or $9$.

Existence
$8712 = 4 \times 2178$

$9801 = 9 \times 1089$