  The nature, composition, abundance, and size distribution of dust in galaxies
is determined by the rate at which it is created in the different stellar
sources and destroyed by interstellar shocks. Because of their extensive
wavelength coverage, proximity, and nearly face-on geometry, the Magellanic
Clouds (MCs) provide a unique opportunity to study these processes in great
detail. In this paper we use the complete sample of supernova remnants (SNRs)
in the MCs to calculate the lifetime and destruction efficiencies of silicate
and carbon dust in these galaxies. We find dust lifetimes of 22 +- 13 Myr (30
+- 17 Myr) for silicate (carbon) grains in the LMC, and 54 +- 32 Myr (72 +- 43
Myr) for silicate (carbon) grains in the SMC. The significantly shorter
lifetimes in the MCs, as compared to the Milky Way, are explained as the
combined effect of their lower total dust mass, and the fact that the
dust-destroying isolated SNe in the MCs seem to be preferentially occurring in
regions with higher than average dust-to-gas (D2G) mass ratios. We also
calculate the supernova rate and the current star formation rate in the MCs,
and use them to derive maximum dust injection rates by asymptotic giant branch
stars and core collapse supernovae. We find that the injection rates are an
order of magnitude lower than the dust destruction rates by the SNRs. This
supports the conclusion that, unless the dust destruction rates have been
considerably overestimated, most of the dust must be reconstituted from
surviving grains in dense molecular clouds. More generally, we also discuss the
dependence of the dust destruction rate on the local D2G mass ratio, the
ambient gas density and metallicity, as well as the application of our results
to other galaxies and dust evolution models.
