Typical continuum extrapolations in lattice QCD treat lattice artifacts as a classical power $a^n$ in the lattice spacing $a$. In an asymptotically free theory like lattice QCD one has quantum corrections of the form $a^n[\alpha(1/a)]^{\hat{\gamma}}$. The leading logarithmic corrections for some lattice actions are presented for massless lattice QCD. Impact of these corrections on continuum extrapolations is discussed.