Subset Sum Problem and hard looking instances that are not really hard
In my opinion, this is an utter triviality, so unimportant that no one would remark on it.   Furthermore, the chance that $t$ numbers chosen at random would have gcd > 1 is vanishingly small once $t$ is large.  (There is an explicit formula, which says that t integers chosen at random from the interval [1..n] will have gcd 1 with probability tending to $1/\zeta(t)$ as $n$ gets large.)