The lowest common denominator, or LCD, is trying to refine something to the most finite and simple representation possible. There is the mathematical concept, but I'm referring more to a theoretical concept of trying to get to simplicity.
Getting to the LCD is a function of time. The process is difficult to get to simplicity in one brainstorming session or meeting. The process is usually a bit of brainstorming, going out and getting some different inputs, testing your thinking, and breaking down some more, and rinse and repeat.
Getting to the LCD is breaking down the exact thing you want to achieve. The process is about deconstructing, both words and concepts, to the core of the issue. The process is isolating the key concepts that make up 90% of what you're trying to achieve. Getting to the LCD is achieving clarity.
Getting to the LCD is a union of theory and action. The LCD is the one concept that makes up 90% of what you're trying to achieve. The next step then is to take that concept and find the most direct way to achieve that.