How carries the sense of measure—of quantity, amount or degree—in itself, and takes an adjective or adverb to define what is to be measured:
How quickly did he run? ... you are asking for the measure of quickness, a speed.
How much money did he have? ... you are asking for the measure of muchness, an amount.
How many hamburgers can he eat? ... you are asking for the measure of manyness, a number.
How big is his house? ... you are asking for the measure of bigness, a size.
So when you ask "How common", there is no need for another adjective to specify that you are asking for a measure of commonness. That's what How? means, all by itself.
Consequently, How much common is not idiomatic English.