Relative mmp without $ \mathbb{Q} $-factoriality

We consider the minimal model program for varieties that are not \begin{document}$ \mathbb{Q}$\end{document} -factorial. We show that, in many cases, its steps are simpler than expected. The main applications are to log terminal singularities, removing the earlier \begin{document}$ \mathbb{Q} $\end{document} -factoriality assumption from several theorems of Hacon-Witaszek and de Fernex-Kollár-Xu.