Given $n$ natural numbers $p_1$, $p_2$, ... $p_n$ find numbers $q_1$, $q_2$, ... $q_n$ that are pairwise coprimes such that $p_i$ ≤ $q_i$ and such that $\prod_{i=1..n} q_i$ is smallest possible.
I come from programing background. When I try to phrase this in my computer science language, then the question would be: I have integer sided hyper rectangle. How do I find smallest (with respect to volume) integer sided hyper rectangle which contains my hyper rectangle such that greatest common divisor of any two side lengths equals to one.