  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 $\Lambda_c^+ \rightarrow \Lambda K^+\pi^+\pi^-$ decay
with a significance of $3.1\sigma$, based on $e^+e^-$ annihilation data
recorded by the BESIII detector at the BEPCII collider. The data correspond to
an integrated luminosity of $6.4~{\rm fb^{-1}}$, in the center-of-mass energy
range from $4.600~{\rm GeV}$ to $4.950~{\rm GeV}$. We determine the branching
fractions of $\Lambda_c^+ \rightarrow \Lambda K^+\pi^0$ and $\Lambda_c^+
\rightarrow \Lambda K^+\pi^+\pi^-$ relative to their Cabibbo-favored
counterparts to be $\frac{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda
K^+\pi^0)}{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda \pi^+\pi^0)} =
(2.09\pm0.39_{\mathrm{stat.}}\pm0.07_{\mathrm{syst.}}) \times 10^{-2}$ and
$\frac{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda
K^+\pi^+\pi^-)}{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda \pi^+\pi^+\pi^-)} =
(1.13\pm0.41_{\mathrm{stat.}}\pm0.06_{\mathrm{syst.}}) \times 10^{-2}$,
respectively. Moreover, by combining our measured result with the world average
of $\mathcal{B}(\Lambda^+_c\to \Lambda\pi^+\pi^0)$, we obtain the branching
fraction $\mathcal{B}(\Lambda_c^+ \to \Lambda K^+\pi^0) =
(1.49\pm0.27_{\mathrm{stat.}}\pm0.05_{\mathrm{syst.}}\pm0.08_{\mathrm{ref.}})
\times 10^{-3}$. This result significantly departs from theoretical predictions
based on quark $SU(3)$ flavor symmetry, which is underpinned by the presumption
of meson pair $S$-wave amplitude dominance.
