In this paper we present a study and comparison of the star formation rates (SFR) in the fields around NGC 1898 and NGC 2154, two intermediate-age star clusters located in very different regions of the Large Magellanic Cloud. We also present a photometric study of NGC 1898, and of seven minor clusters which happen to fall in the field of NGC 1898, for which basic parameters were so far unknown. We do not focus on NGC 2154, because this cluster was already investigated in Baume et al. 2007, using the same theoretical tools. The ages of the clusters were derived by means of the isochrone fitting method on their $clean$ color-magnitude diagrams. Two distinct populations of clusters were found: one cluster (NGC 2154) has a mean age of 1.7 Gyr, with indication of extended star formation over roughly a 1 Gyr period, while all the others have ages between 100 and 200 Myr. The SFRs of the adjacent fields were inferred using the downhill-simplex algorithm. Both SFRs show enhancements at 200, 400, 800 Myr, and at 1, 6, and 8 Gyr. These bursts in the SFR are probably the result of dynamical interactions between the Magellanic Clouds (MCs), and of the MCs with the Milky Way.