  We prove that if $L(G)$ immerses $K_t$ then $L(mG)$ immerses $K_{mt}$, where
$mG$ is the graph obtained from $G$ by replacing each edge in $G$ with a
parallel edge of multiplicity $m$. This implies that when $G$ is a simple
graph, $L(mG)$ satisfies a conjecture of Abu-Khzam and Langston. We also show
that when $G$ is a line graph, $G$ has a $K_t$-immersion iff $G$ has a
$K_t$-minor whenever $t\leq 4$, but this equivalence fails in both directions
when $t \geq 5$.
