"But please, if you can form a logical explanation as to how you have come to compare the currents from the idea of Voltage, you will have provided an answer to this question."
I do not understand what you say here, but here is my answer. You have use the fact that Ohm's law is linear, and we have only linear elements in our circuit, so you can use principle of superposition.
That is, assume only one battery is switched on, and calculate the resulting currents through the resistors (tedious, but easy). Now do this for every one of the four batteries present. After you have done this, sum up all the contributing currents through each resistor.
As an example, let's assume we have switched on the topmost battery V only.
You easily see that the currents are
through K: zero
through L: V/R (flowing from right to left)
through M: V/R (flowing from right to left)
Now do this kind of analysis for the remaining three batteries.
EDIT: Okay, I carry out the remaining analysis to be done.
The net contributions are:
current through K: 0 + (-V/R) + 0 + 0 = - V/R
current through L: (V/R) + (-V/R) + 0 + 0 = 0 (easy to see, since all batteries have the same potential and L connects to cathodes on both ends).
current through M: (V/R) + (-V/R) + (-V/R) + (-V/R) = -2V/R (positive being from right to left)
the circuit diagram you have shared with us is easy enough that you can read the current just off the diagram, but the kind of analysis I have used using linear superposition should help when there is a more complex one.