Observations of the Cabibbo-Suppressed decays $Λ_{c}^{+}\to nπ^{+}π^{0}$, $nπ^{+}π^{-}π^{+}$ and the Cabibbo-Favored decay $Λ_{c}^{+}\to nK^{-}π^{+}π^{+}$
Using electron-positron annihilation data samples corresponding to an integrated luminosity of 4.5 $\rm{{fb}^{-1}}$, collected by the BESIII detector in the energy region between $4600$ MeV and $4699$ MeV, we report the first observations of the Cabibbo-suppressed decays $Λ_c^+\to nπ^+π^0$, $Λ_c^+\to nπ^+π^-π^+$, and the Cabibbo-favored decay $Λ_c^+\to nK^-π^+π^+$ with statistical significances of $7.9σ$, $7.8σ$, and $>10σ$, respectively. The branching fractions of these decays are measured to be $\mathcal{B}(Λ_{c}^{+}\rightarrow nπ^{+}π^{0})=(0.64\pm0.09\pm0.02)\%$, $\mathcal{B}(Λ_{c}^{+}\rightarrow nπ^{+}π^{-}π^{+})=(0.45\pm0.07\pm0.03)\%$, and $\mathcal{B}(Λ_{c}^{+}\rightarrow nK^{-}π^{+}π^{+})=(1.90\pm0.08\pm0.09)\%$, where the first uncertainties are statistical and the second are systematic. We find that the branching fraction of the decay $Λ_{c}^{+}\rightarrow nπ^{+}π^{0}$ is about one order of magnitude higher than that of $Λ_{c}^{+}\rightarrow nπ^{+}$.