Molar conductivity $\Lambda_m$ of an electrolytic solution is related to its conductivity $\kappa$ and molar concentration $c$ by:

$\Lambda_m = \dfrac{\kappa}{c}$. With $\kappa$ in $\text{S cm}^{-1}$ and $c$ in $\text{mol cm}^{-3}$, $\Lambda_m$ comes out in $\text{S cm}^2\,\text{mol}^{-1}$. If $c$ is in $\text{mol L}^{-1}$, a factor of $1000\,\text{cm}^3/\text{L}$ is folded in, giving $\Lambda_m = 1000\kappa/c$.