Finding path, the sum of whose numbered edges is 48

Finding path, the sum of whose numbered edges is 48

Let $G$ be a graph with vertices $\{1,...,10\}$. Two vertices $a,b$ have
an edge if $a|b$ or $b|a$. Find a path in $G$ so that the sum of the
corners in the path equals 48.
I solved this using "brute force", $9-3-6-2-8-4-1-10-5$, but is there a
more efficient way? In particular one that doesn't rely on drawing the
graph in a clever way.