© 2019 authors. Published by the American Physical Society. We find constraints on R-parity violating (RPV) couplings of the minimal supersymmetric Standard Model, using Drell-Yan differential cross sections at the LHC. Specifically, we look at the constraints on λ′LQDc couplings from monolepton and dilepton data published by ATLAS, with either electrons or muons in the final state. Out of the 18 RPV couplings to which the LHC is at least potentially sensitive by this technique, we find new limits on 12 (or 13) of them, for squarks masses above 1 (or 2) TeV. We also show that one can employ our techniques to achieve significantly stronger bounds at a high-luminosity upgrade of the LHC.