Why is voltage gain highest in common base transistors whereas lowest in common collector transistors? Although the common base transistors have current gain lowest and the common collector transistors have current gain highest.
 A: There are a couple of basic facts about bipolar junction transistors (BJT's) that could help figure that out. 
First is that the ratio between the collector and base currents, beta, is roughly the same for all configurations (CE, CC and CB) and is typically on the order of hundreds, i.e., the collector current is typically much higher than the base current. 
Second, of course, is that the sum of all transistor currents is equal zero or, if we assume that the current originates from the emitter and splits into the collector and base currents, we can say that Ie = Ic+Ib.
From here we can try to ballpark voltage and current gains for different configurations.
In the common base configuration, the input current is the emitter current and the output current is the collector current. 

Since, according to the equation above, Ic=Ie-Ib, we have to conclude that the current gain in this configuration is always a little less than 1. 
As for the CB voltage gain, it is controlled by the load resistor, RL, and can be as low as zero and as high as the transistor can withstand. Still, we can say that CB voltage gain can be made high. 
In the common collector configuration, the input current is the base current and the output current is the emitter current. 

Since Ie = Ic+Ib or Ie = Ib*(beta+1), the current gain Ie/Ib = beta + 1, and therefore is high.
As for the CC voltage gain, it is limited by the fact that the load resistor is inserted between the emitter and the ground. As a result, the output voltage (the voltage on the load resistor) is equal to the difference between the input voltage and the base-emitter voltage (which, for simplicity, could be considered a constant value around 0.6V): Vout = Vin-Vbe. From here we can see that the output voltage is always smaller than the input voltage and therefore the CC voltage gain is always less than 1.
NOTE: For simplicity, we are not taking into account the input resistors Rin. 
So we can see that, even in the most basic analysis, the voltage and current gains are very much dependent on the way a transistor is connected - not only on the intrinsic transistor characteristics. Therefore, there should not be any expectation that a high voltage gains should automatically imply a high or low current gain. 
Notice: the drawings have been copied from the Electronics Tutorials website.
