The decays Λb0→Λc+D(∗)0K− and Λb0→Λc+Ds∗− are observed for the first time, in proton-proton collision data at s=13TeV, corresponding to an integrated luminosity of 5.4fb−1 collected with the LHCb detector. Their ratios of branching fractions with respect to the Λb0→Λc+Ds− mode are measured to be B(Λb0→Λc+Ds−)B(Λb0→Λc+D0K−)B(Λb0→Λc+Ds−)B(Λb0→Λc+D∗0K−)B(Λb0→Λc+Ds−)B(Λb0→Λc+Ds∗−)=0.1908−0.0034+0.0036−0.0018+0.0016±0.0038,=0.589−0.017+0.018−0.018+0.017±0.012,=1.668±0.022−0.055+0.061,where the first uncertainties are statistical, the second systematic, and the third, for the Λb0→Λc+D(∗)0K− decays, are due to the uncertainties on the branching fractions of the Ds−→K−K+π− and D0→K+π− decay modes. The measured branching fractions probe factorization assumptions in effective theories and provide the normalization for future pentaquark searches in Λb0→Λc+D(∗)0K− decay channels.