We study the evolution of three fields in the outer Large Magellanic Cloud (LMC) disc (Rgc = 3.5-6.2 kpc). Their star formation history indicates a stellar population gradient such that younger stellar populations are more centrally concentrated. We identify two main star-forming epochs, separated by a period of lower activity between ≃7 and ≃4 Gyr ago. Their relative importance varies from a similar amount of stars formed in the two epochs in the innermost field to only 40 per cent of the stars formed in the more recent epoch in the outermost field. The young star-forming epoch continues to the present time in the innermost field, but lasted only till ≃0.8 and 1.3 Gyr ago at Rgc = 5.5° and 7.7°, respectively. This gradient is correlated with the measured H I column density and implies an outside-in quenching of the star formation, possibly related to a variation of the size of the H I disc. This could either result from gas depletion due to star formation or ram-pressure stripping, or from to the compression of the gas disc as ram pressure from the Milky Way halo acted on the LMC interstellar medium. The latter two situations may have occurred when the LMC first approached the Milky Way.