We measure the branching ratios of the Cabibbo-suppressed decays Λc+→ΛK+ and Λc+→Σ0K+ relative to the Cabibbo-favored decay modes Λc+→Λπ+ and Λc+→Σ0π+ to be 0.044±0.004(stat.)±0.003(syst. ) and 0.038±0.005(stat.)±0.003(syst.), respectively. We set an upper limit on the branching ratio at the 90% confidence level for Λc+→ΛK+π+π- of 4.1×10-2 relative to Λc+→Λπ+, and for Λc+→Σ0K+π+π- of 2.0×10-2 relative to Λc+→Σ0π+. We also measure the branching fraction for the Cabibbo-favored mode Λc+→Σ0π+ relative to Λc+→Λπ+ to be 0.977±0.015(stat.) ±0.051(syst.). This analysis was performed using a data sample with an integrated luminosity of 125fb-1 collected by the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. © 2007 The American Physical Society.