  Extragalactic black hole X-ray binaries LMC X-1 and LMC X-3 are the
persistent sources, usually found in soft spectral state. We present the
results from spectral and timing study of these sources using MAXI, NICER,
NuSTAR and AstroSat observations carried out during 2014-2020. Study of
long-term MAXI lightcurve shows that the fractional variability of flux in
2-10keV is moderate ($\sim$20%) in LMCX-1 and high ($\sim$50%) in LMCX-3. The
energy spectra of both sources are characterized by a disc blackbody and a
Comptonization component with LMCX-1 having an additional Fe-line emission
feature. NICER (0.3-10keV), NuSTAR (3.0-40keV) and AstroSat (0.5-20keV)
spectral analysis collectively show that LMC X-1 remained in the soft state
(disc flux contribution $f_{disc}>80$%, photon index$\Gamma\sim2.06-4.08$)
throughout 2014-2020. Mass accretion rate, $\dot{M}$ of LMC X-1 calculated from
bolometric luminosity (0.1-50keV) is found to be within
$0.07-0.24\dot{M}_{Edd}$ (Eddington mass accretion rate). Although LMC X-3
remained in the soft state ($f_{disc}>95\%,\Gamma\sim2.3$) during most of the
time, it exhibits transition into intermediate
($f_{disc}=47-73\%,\Gamma\sim2.02-2.36$) and hard state
($f_{disc}\sim26\%,\Gamma\sim1.6$). $\dot{M}$ of LMC X-3 through different
spectral states varies within $0.01-0.42\dot{M}_{Edd}$. Temporal study show
that the Power Density Spectra (PDS) in 0.3-10keV follow a red-noise with rms
of 2% for LMC X-1 and in case of LMC X-3, it is 0.08-2.35% during the soft
state, but relatively high in the intermediate(3.05-4.91%) and hard
state($\sim$17.06%). From continuum-fitting method we constrain spin of LMC X-1
and LMC X-3 to be within 0.85-0.94 and 0.16-0.33 respectively and from Fe-line
fitting method, spin of LMC X-1 is found to be 0.93-0.94. Finally, we discuss
the implication of our findings in the context of accretion disc dynamics
around the vicinity of the BHs.
