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 Ca II triplet , from which we derived individual radial velocities ( RVs ) and metallicities . From cluster members we derived mean RVs of RV _ { NGC 1928 } = 249.58 \pm 4.65 km/s and RV _ { NGC 1939 } = 258.85 \pm 2.08 km/s , and mean metallicities of [ Fe/H ] _ { NGC 1928 } = -1.30 \pm 0.15 dex and [ Fe/H ] _ { NGC 1939 } = -2.00 \pm 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 .