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 \pm 13 Myr ( 30 \pm 17 Myr ) for silicate ( carbon ) grains in the LMC , and 54 \pm 32 Myr ( 72 \pm 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 ( AGB ) stars and core collapse supernovae ( CCSNe ) . 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 and the ambient gas density and metallicity , as well as the application of our results to other galaxies and dust evolution models .