We present results obtained from spectroscopic observations of red giants located in the fields of the Large Magellanic Cloud (LMC) globular clusters (GCs) NGC 1928 and NGC 1939. We used the GMOS and AAOmega+2dF spectrographs to obtain spectra centred on the CaII triplet, from which we derived individual radial velocities (RVs) and metallicities. From cluster members we derived mean RVs of RV_NGC1928=249.58+-4.65 km/s and RV_NGC939=258.85+-2.08 km/s, and mean metallicities of [Fe/H]_NGC1928=-1.30+-0.15 dex and [Fe/H]_NGC1939=-2.00+-0.15 dex. We found that both GCs have RVs and positions consistent with being part of the LMC disc, so that we rule out any possible origin but that in the same galaxy. By computing the best solution of a disc that fully contains each GC, we obtained circular velocities for the 15 known LMC GCs. We found that 11/15 of the GCs share the LMC rotation derived from $HST$ and $Gaia$ DR2 proper motions. This outcome reveals that the LMC disc existed since the very early epoch of the galaxy formation and experienced the steep relatively fast chemical enrichment shown by its GC metallicities. The four remaining GCs turned out to have circular velocities not compatible with an in situ cluster formation, but rather with being stripped from the SMC.
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