Logical reasoning behind the formula for molar conductance of an electrolyte
For most physical properties of substances, it's useful to know how those properties depend on other parameters.  For example, the various coefficients of thermal expansion (CTEs) indicate how rapidly the dimension(s) of a substance change when the temperature is changed by a given amount. A common CTE used when working with materials is the linear CTE:

$$
\alpha_\mathrm L = {1\over L} {dL \over dT}
$$

When thermal expansion occurs, if the temperature change is relatively small the amount of thermal expansion is roughly proportional to the original length $L$. So, the definition of $\alpha_\mathrm L$ divides the length dependence $dL/dT$ by $L$ to yield a parameter that is approximately constant within a particular temperature range.

A similar rationale underlies the definition of the molar conductance (also called the 'molar conductivity') as:

$$
\Lambda_\mathrm m = {\kappa \over c}
$$

The conductivity $\kappa$ of an electrolyte is a strong function of the concentration $c$ of the electrolyte of interest. However, for electrolytes containing only strong acids and/or bases (or salts of these), $\kappa$ is nearly a linear function of $c$ over a very wide concentration range, and thus $\Lambda_\mathrm m$ for these electrolytes is nearly constant.

Thus, for species that show this strong linearity, defining $\mathbf{\Lambda_m}\equiv\kappa / c$ is useful because a single $\mathbf{\Lambda_m}$ value can be employed to calculate the absolute conductivity $\mathbf\kappa$ across a wide range of electrolyte concentrations $c$, as:

$$\kappa = \Lambda_\mathrm m c$$