What is exactly molar conductivity?
Say conductivity of the electrolyte is represented by $\kappa$, molar conductivity by $G$, resistance by $R$ and resistivity of the electrolyte by $\rho$
I'm assuming you know the definitions to the above since you've asked this question.
Now, resistance $R$ = $\frac{\rho\space l}{A}$ where $l$ is the length of the conductor and $A$ is the area of cross section.
For an electrolyte, $l$ can be taken equal to the distance between the electrodes and $A$ can be taken as the surface area of the electrodes.
Since conductivity is the reciprocal of resistivity ($\kappa$ = $\frac{1}{\rho}$),
$R$ = $\frac{\space l}{\kappa\space A}$
Reciprocating both sides,
$\frac{1}{R}$ = $\frac{\kappa\space A}{l}$
Since molar conductitivy is defined as the conductance of the entire solution having 1 mole of electrolyte dissolved in it and conductance is $\frac{1}{R}$,
$G$ = $\frac{\kappa\space A}{l}$
where $G$ is molar conductivity