We present the results obtained from detailed spectral and timing studies of extragalactic black hole X-ray binaries LMC X-1 and LMC X-3, using simultaneous observations with Nuclear Spectroscopic Telescope Array (NuSTAR) and Neil Gehrels Swift observatories. The combined spectra in the 0.5-30 keV energy range, obtained between 2014 and 2019, are investigated for both sources. We do not find any noticeable variability in 0.5-30 keV light curves, with 0.1-10 Hz fractional rms estimated to be 2.5 and thermal emission fraction, fdisc > 80 per cent. An Fe Kα emission line is detected in the spectra of LMC X-1, though no such feature is observed in the spectra of LMC X-3. From the spectral modelling, the spins of the black holes in LMC X-1 and LMC X-3 are estimated to be in the range of 0.92-0.95 and 0.19-0.29, respectively. The accretion efficiency is found to be, η ∼0.13 and η ∼0.04 for LMC X-1 and LMC X-3, respectively.