What do I mean when I use the phrase " the lowest common denominator"?

I use the phrase to mean, making a decision or "rule/law" for ALL based on the behavior of a FEW.

EX: Three children in class are loud, disruptive and inciting the entire class to misbehave. Therefore the ENTIRE class is kept inside at recess instead of just those inciting the misbehavior.

Some people drink irresponsibly, therefore the WHOLE COUNTY must be dry.