Smallest Triplet of Integers whose Product with Divisor Count are Equal

Theorem
Let $\tau \left({n}\right)$ denote the $\tau$ function: the number of divisors of $n$.

The smallest set of $3$ integers $T$ such that $m \tau \left({m}\right)$ is equal for each $m \in T$ is:
 * $\left\{ {168, 192, 224}\right\}$