\begin{document}$ ^{-1} $\end{document}, collected by the BESIII detector in the energy region between \begin{document}$ 4599.53\; \,{\rm{MeV}} $\end{document} and \begin{document}$ 4698.82\; \,{\rm{MeV}} $\end{document}, we report the first observations of the Cabibbo-suppressed decays \begin{document}$ \Lambda_c^+\to n\pi^+\pi^0 $\end{document}, \begin{document}$ \Lambda_c^+\to n\pi^+\pi^-\pi^+ $\end{document}, and the Cabibbo-favored decay \begin{document}$ \Lambda_c^+\to nK^-\pi^+\pi^+ $\end{document} with statistical significances of \begin{document}$ 7.9\sigma $\end{document}, \begin{document}$ 7.8\sigma $\end{document}, and \begin{document}$ >10\sigma $\end{document}, respectively. The branching fractions of these decays are measured to be \begin{document}$\mathcal{B}(\Lambda_{c}^{+}\rightarrow n\pi^{+}\pi^{0})=(0.64\pm0.09\pm0.02)$\end{document}%, \begin{document}$\mathcal{B}(\Lambda_{c}^{+}\rightarrow n\pi^{+}\pi^{-}\pi^{+})=(0.45\pm 0.07\pm $\end{document}\begin{document}$ 0.03)$\end{document}%, and \begin{document}$\mathcal{B}(\Lambda_{c}^{+}\rightarrow nK^{-}\pi^{+}\pi^{+})=(1.90\pm0.08\pm0.09)$\end{document}%, where the first uncertainties are statistical and the second are systematic. We find that the branching fraction of the decay \begin{document}$ \Lambda_{c}^{+}\rightarrow n\pi^{+}\pi^{0} $\end{document} is about one order of magnitude higher than that of \begin{document}$ \Lambda_{c}^{+}\rightarrow n\pi^{+} $\end{document}."> Observations of the Cabibbo-Suppressed decays <inline-formula><tex-math id="M1">\begin{document}${\boldsymbol \Lambda_{\boldsymbol c}^{\bf +}\to\boldsymbol n\pi^{\bf +}\boldsymbol\pi^{\bf 0}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/1c04bdd3-1095-470c-9654-83420a1c7367/CPC-2022-0494_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/1c04bdd3-1095-470c-9654-83420a1c7367/CPC-2022-0494_M1.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}${\boldsymbol n\pi^{+}\boldsymbol\pi^{\bf -}\boldsymbol\pi^{\bf +} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/1c04bdd3-1095-470c-9654-83420a1c7367/CPC-2022-0494_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/1c04bdd3-1095-470c-9654-83420a1c7367/CPC-2022-0494_M2.png"/></alternatives></inline-formula> and the Cabibbo-Favored decay <inline-formula><tex-math id="M3">\begin{document}${\boldsymbol \Lambda_{\boldsymbol c}^{\bf +}\to \boldsymbol nK^{\bf -}\boldsymbol\pi^{\bf +}\boldsymbol\pi^{\bf +} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/1c04bdd3-1095-470c-9654-83420a1c7367/CPC-2022-0494_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/1c04bdd3-1095-470c-9654-83420a1c7367/CPC-2022-0494_M3.png"/></alternatives></inline-formula> -
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