Recent study about the supernova remnants (SNRs) in the Large Magellanic Cloud (LMC) shows that there is an interesting relationship between the X-ray luminosity and the size of the SNRs. Core-collapse (CC) SNRs of similar sizes may have distinct magnitudes of luminosity. We want to figure out the reason. Thus, we speculate that high X-ray emission is produced in a high ambient density, whereas low X-ray emission in a low one. Both X-ray and Hα emissivities are functions of temperature and density of the emitting gas, but the functions of form are different. We use X-ray and Hα surface brightnesses to examine the physical conditions of the SNRs and investigate the origin of the X-ray luminosity and size relationship.