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We have endeavoured to understand the formation and evolution of the blackhole (BH) X-ray binary LMC X-3. We estimate the properties of the system at 4evolutionary stages: 1) at the Zero Age Main Sequence (ZAMS), 2) just prior tothe supernova (SN) explosion of the primary, 3) just after the SN, and 4) atthe moment of RLO onset.We use a hybrid approach, combining detailed stellarstructure and binary evolution calculations with approximate populationsynthesis models. This allows us to estimate potential natal kicks and theevolution of the BH spin. In the whole analysis we incorporate as modelconstraints the most up-to-date observational information, encompassing thebinary's orbital properties, the companion star mass, effective temperature,surface gravity and radius, as well as the black hole's mass and spin. We findthat LMC X-3 began as a ZAMS system with the mass of the primary star in therange $M_{\rm{1,ZAMS}}$ = 22-31 $\rm{M_{\odot}}$ and a secondary star of$M_{\rm{2,ZAMS}} = 5.0-8.3M_{\odot}$, in a wide ($P_{ZAMS} \gtrsim 2.000\, \rmdays$) and eccentric ($e_{\rm{ZAMS}} \gtrsim 0.23$) orbit. Just prior to theSN, the primary has a mass of $M_{\mathrm{1,preSN}} = 11.1-18.0\,\rmM_{\odot}$, with the secondary star largely unaffected. The orbital perioddecreases to $0.6-1.7\, \rm days$, and is still eccentric $0 \leqe_{\rm{preSN}} \leq 0.44$. We find that a symmetric SN explosion with no orsmall natal kicks (a few tens of $\rm km\, s^{-1}$) imparted on the BH cannotbe formally excluded, however, large natal kicks in excess of $\gtrsim 120\,\rm km\, s^{-1}$ increase the estimated formation rate by an order ofmagnitude. Following the SN, the system has a BH $M_{\mathrm{BH,postSN}} =6.4-8.2\,\rm M_{\odot}$ and is put into an eccentric orbit. At the RLO onsetthe orbit is circularised and it has an orbital period of $P_{\rm{RLO}} =0.8-1.4\,\rm days$.

Unraveling the Formation History of the Black Hole X-ray Binary LMC X-3 from ZAMS to Present