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We present the Large Hadron Collider (LHC) discovery potential in the Z' sector of a U(1)_{B-L} enlarged Standard Model also encompassing three heavy Majorana neutrinos, for \sqrt{s}=7 centre-of-mass energy, considering both the Z'_{B-L}\rightarrow e^+e^- and Z'_{B-L}\rightarrow μ^+μ^- decay channels. Electrons provide a higher sensitivity to smaller couplings at small Z'_{B-L} boson masses than do muons. The run of the LHC at \sqrt{s}=7 TeV, assuming at most \int \mathcal{L} \sim 1 fb^{-1}, will be able to give similar results to those that will be available soon at the Tevatron in the lower mass region, and to extend them for a heavier M_{Z'}. A 5σdiscovery could be possible up to M_{Z'}=1.2(0.9) TeV at the LHC(Tevatron), while a 2σexclusion at the LHC could be possible up to M_{Z'}=1.6 TeV. The new gauge coupling g'_1 can been probed, at 5σ, down to \sim (3 ÷4) \cdot 10^{-2} with electrons and down to \sim (4 ÷5) \cdot 10^{-2} with muons, both at the LHC and at the Tevatron, for M_{Z'}=600 GeV. The Z' boson in this model exhibits novel signatures at the LHC, as multi-lepton and multi-jet decays via heavy neutrinos, that allow one to measure the heavy neutrino masses involved. Lastly, the simultaneous measurement of both the heavy neutrino mass and decay length (over a large region of parameter space, the heavy neutrinos are rather long-lived particles) enables an estimate of the absolute mass of the parent light neutrino.