Two fractions cannot be added while their pieces are different sizes. So you look for one number that every bottom number fits into, cut everything into pieces of that size, and suddenly the fractions can sit side by side. That is the whole picture: the one thing underneath that works for all of them. English then carries that picture out of the maths class. Put several people or stories side by side and the thing found underneath all of them is the common denominator — and if you go as low as you must to fit everybody in, you get the lowest one.
Two branches
數學上的公分母
這是這個詞的原生地，也是整個畫面的來源。後面兩個意思都靠這個畫面在支撐，所以先看懂分數這一邊，另一邊就不必硬背。
noun · B1
In maths, a number that the bottom number of each fraction in a set can divide into exactly, so that all the fractions can be rewritten with the same bottom number and then added, taken away, or compared.
公分母
大家底下共有的那一點
把分數換成人、故事、案例，畫面照搬：先並排，再找底下共通的那一個。這一支跟數學那一支長得一模一樣，差別只在加了一個 lowest 之後，整句話就從中性的觀察變成帶貶意的評論。
noun · B2
A quality, attitude, or feature that every member of a group has, so that it is the one thing you find in all of them when you look at them side by side.
共同點