We investigate the effects of supergiant shells (SGSs) and their interaction on dense molecular clumps by observing the Large Magellanic Cloud (LMC) star-forming regions N48 and N49, which are located between two SGSs, LMC 4 and LMC 5. 12CO (J = 3-2, 1-0) and 13CO(J = 1-0) observations with the ASTE and Mopra telescopes have been carried out toward these regions. A clumpy distribution of dense molecular clumps is revealed with 7 pc spatial resolution. Large velocity gradient analysis shows that the molecular hydrogen densities (n(H2)) of the clumps are distributed from low to high density (103-105 cm-3) and their kinetic temperatures (T kin) are typically high (greater than 50 K). These clumps seem to be in the early stages of star formation, as also indicated from the distribution of Hα, young stellar object candidates, and IR emission. We found that the N48 region is located in the high column density H I envelope at the interface of the two SGSs and the star formation is relatively evolved, whereas the N49 region is associated with LMC 5 alone and the star formation is quiet. The clumps in the N48 region typically show high n(H2) and T kin, which are as dense and warm as the clumps in LMC massive cluster-forming areas (30 Dor, N159). These results suggest that the large-scale structure of the SGSs, especially the interaction of two SGSs, works efficiently on the formation of dense molecular clumps and stars.