We report on the observation of two Feshbach resonances in collisions between ultracold
6Li and
87Rb atoms in their respective hyperfine ground states $\ensuremath{\mid}F,{m}_{F}⟩=\ensuremath{\mid}1∕2,1∕2⟩$ and \ensuremath{\mid}1,1⟩. The resonances show up as trap losses for the
6Li cloud induced by inelastic Li-Rb-Rb three-body collisions. The magnetic field values where they occur represent important benchmarks for an accurate determination of the interspecies interaction potentials. A broad Feshbach resonance located at
1066.92G opens interesting prospects for the creation of ultracold heteronuclear molecules. We furthermore observe a strong enhancement of the narrow
p-wave Feshbach resonance in collisions of
6Li atoms at
158.55G in the presence of a dense
87Rb cloud. The effect of the
87Rb cloud is to introduce Li-Li-Rb three-body collisions occurring at a higher rate than Li-Li-Li collisions.