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We present the first observation of the singly Cabibbo-suppressed decay$\Lambda_c^+ \rightarrow \Lambda K^+\pi^0$ with a significance of $5.7\sigma$and the first evidence of $\Lambda_c^+ \rightarrow \Lambda K^+\pi^+\pi^-$ decaywith a significance of $3.1\sigma$, based on $e^+e^-$ annihilation datarecorded by the BESIII detector at the BEPCII collider. The data correspond toan integrated luminosity of $6.4~{\rm fb^{-1}}$, in the center-of-mass energyrange from $4.600~{\rm GeV}$ to $4.950~{\rm GeV}$. We determine the branchingfractions of $\Lambda_c^+ \rightarrow \Lambda K^+\pi^0$ and $\Lambda_c^+\rightarrow \Lambda K^+\pi^+\pi^-$ relative to their Cabibbo-favoredcounterparts to be $\frac{\mathcal{B}(\Lambda_c^+ \rightarrow \LambdaK^+\pi^0)}{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda \pi^+\pi^0)} =(2.09\pm0.39_{\mathrm{stat.}}\pm0.07_{\mathrm{syst.}}) \times 10^{-2}$ and$\frac{\mathcal{B}(\Lambda_c^+ \rightarrow \LambdaK^+\pi^+\pi^-)}{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda \pi^+\pi^+\pi^-)} =(1.13\pm0.41_{\mathrm{stat.}}\pm0.06_{\mathrm{syst.}}) \times 10^{-2}$,respectively. Moreover, by combining our measured result with the world averageof $\mathcal{B}(\Lambda^+_c\to \Lambda\pi^+\pi^0)$, we obtain the branchingfraction $\mathcal{B}(\Lambda_c^+ \to \Lambda K^+\pi^0) =(1.49\pm0.27_{\mathrm{stat.}}\pm0.05_{\mathrm{syst.}}\pm0.08_{\mathrm{ref.}})\times 10^{-3}$. This result significantly departs from theoretical predictionsbased on quark $SU(3)$ flavor symmetry, which is underpinned by the presumptionof meson pair $S$-wave amplitude dominance.

First observation of $\Lambda_c^+\rightarrow\Lambda K^+\pi^0$ and evidence of $\Lambda_c^+\rightarrow\Lambda K^+\pi^+\pi^-$