  We study the $\Lambda$-nucleon ($\Lambda N$) force by using lattice QCD. The
Bethe-Salpeter amplitude is calculated for the lowest scattering state of the
$\Lambda N$ so as to obtain the $\Lambda N$ potential. The numerical
calculation is twofold: (i) Full lattice QCD by using 2+1 flavor PACS-CS gauge
configurations with, $\beta=1.9$, corresponding to the lattice spacing of
$a=0.0907(13)$ fm, on a $32^3\times 64$ lattice. A set of parameter
$(\kappa_{ud},\kappa_s)=(0.13770,0.13640)$ is used, which corresponds to
$m_\pi\approx 300$ MeV and $m_K\approx 594$ MeV. The spatial lattice volume
corresponds to (2.86 fm)$^3$. (ii) Quenched lattice QCD with $\beta=5.7$, the
lattice spacing of $a=0.1416(9)$ fm, on the $32^3\times48$ lattice. Two sets of
hopping parameters $(\kappa_{ud},\kappa_s)=(0.1665,0.1643),(0.1670,0.1643)$ are
used. The spatial lattice volume is (4.5 fm)$^3$. For the full QCD, we find
that the $\Lambda p$ has a relatively strong (weak) repulsive core in the
$^1S_0$ ($^3S_1$) channel at short distance, while the potential has slight
attractive region at medium distance. The lowest scattering energy in the
finite lattice volume is calculated; Slightly negative values obtained in both
spin channels. For the quenched QCD, we find that the results are qualitatively
in agreement with those in the full QCD calculation.
