Co-prime Composites

$a+b=c$

Let $a,b,c$ be positive composite integers, satisfying the equation above, such that $abc = p_n \#$ for some $n^{th,}$ prime.

What is the least possible value of $c$ ?

Note : $p_n \#$ is primorial, e.g. $p_5 \# = 2•3•5•7•11$ .