Singularity of $\mathbb{Q}$-divisors of multidegree one in multiprojective space

We study singularity of effective $\mathbb{Q}$-divisors on products of projective spaces of multidegree $(1,\mathrm{1...},1)\mathrm{.}$ This generalizes works of Bath, Musta{ţ}{ă} and Walther on singularity of square-free polynomials. We also give a lower bound on the log canonical threshold of a hypersurface in products of projective spaces.