  The Large Magellanic Cloud (LMC) has $\sim$60 confirmed supernova remnants
(SNRs). Because of the known distance, 50 kpc, the SNRs' angular sizes can be
converted to linear sizes, and their X-ray observations can be used to assess
X-ray luminosities ($L_X$). We have critically examined the LMC SNRs' sizes
reported in the literature to determine the most plausible sizes. These sizes
and the $L_X$ determined from \emph{XMM-Newton} observations are used to
investigate their relationship in order to explore the environmental and
evolutionary effects on the X-ray properties of SNRs. We find: (1) Small LMC
SNRs, a few to 10 pc in size, are all of Type Ia with $L_X>10^{36}$ ergs
s$^{-1}$. The scarcity of small core-collapse (CC) SNRs is a result of CCSNe
exploding in the low-density interiors of interstellar bubbles blown by their
massive progenitors during their main sequence phase. (2) Medium-sized (10-30
pc) CC SNRs show bifurcation in $L_X$, with the X-ray-bright SNRs either in an
environment associated with molecular clouds or containing pulsars and pulsar
wind nebulae and the X-ray-faint SNRs being located in low-density interstellar
environments. (3) Large (size$>$30 pc) SNRs show a trend of $L_X$ fading with
size, although the scatter is large. The observed relationship between $L_X$
and sizes can help constrain models of SNR evolution.
