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This paper presents combinations of inclusive and differential measurements of the charge asymmetry (A) in top quark pair events with a lepton+jets signature by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. The data correspond to integrated luminosities of about 5 and 20 fb for each experiment, respectively. The resulting combined LHC measurements of the inclusive charge asymmetry are A = 0.005 ± 0.007 (stat) ± 0.006(syst) at 7 TeV and A = 0.0055 ± 0.0023 (stat) ± 0.0025 (syst) at 8 TeV. These values, as well as the combination of A measurements as a function of the invariant mass of the system at 8 TeV, are consistent with the respective standard model predictions.