a number that can be divided exactly by all the denominators (= numbers under the line) in a group of fractions

12 is a common denominator of 1/3 and 1/4. 12是1／3和1／4的公分母。

something that is the same for all the members of a group and might bring them together

The common denominator was that we had all worked for the same company. 共同点是我们都曾为同一家公司工作。