The ratios of the branching fractions of the decays $Lambda_{c}^{+} rightarrow p pi^{-} pi^{+}$, $Lambda_{c}^{+} rightarrow p K^{-} K^{+}$, and $Lambda_{c}^{+} rightarrow p pi^{-} K^{+}$ with respect to the Cabibbo-favoured $Lambda_{c}^{+} rightarrow p K^{-} pi^{+}$ decay are measured using proton-proton collision data collected with the LHCb experiment at a 7 TeV centre-of-mass energy and corresponding to an integrated luminosity of 1.0 fb$^{-1}$: begin{align*} frac{mathcal{B}(Lambda_{c}^{+} rightarrow p pi^{-} pi^{+})}{mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})} & = (7.44 pm 0.08 pm 0.18),%, frac{mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} K^{+})}{mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})} &= (1.70 pm 0.03 pm 0.03),%, frac{mathcal{B}(Lambda_{c}^{+} rightarrow p pi^{-} K^{+})}{mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})} & = (0.165 pm 0.015 pm 0.005 ),%, end{align*} where the uncertainties are statistical and systematic, respectively. These results are the most precise measurements of these quantities to date. When multiplied by the world-average value for $mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})$, the corresponding branching fractions are begin{align*} mathcal{B}(Lambda_{c}^{+} rightarrow p pi^{-} pi^{+}) &= (4.72 pm 0.05 pm 0.11 pm 0.25) times 10^{-3}, mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} K^{+}) &= (1.08 pm 0.02 pm 0.02 pm 0.06) times 10^{-3}, mathcal{B}(Lambda_{c}^{+} rightarrow p pi^{-} K^{+}) &= (1.04 pm 0.09 pm 0.03 pm 0.05) times 10^{-4}, end{align*} where the final uncertainty is due to $mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})$.
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