In math, fractions can be converted to other equivalent fractions:
1/2 = 3/6 = 6/12
In each case the denominator (the bottom number) changes, but maintains the same proportional relationship to the numerator (the upper number).
To add two fractions that have different denominators, you need to convert them to equivalents that have the same denominator. For example,
1/3 + 1/2 = 2/6 + 3/6 = 5/6
In the above case, 6 is the lowest common denominator for both 1/3 and 1/2. There are other possible denominators, such as 12, but 6 is the lowest.
This concept has been carried over to non-mathematical fields. In that context, the lowest common denominator generally means the simplest thing that all involved parties have in common that can accomplish a goal.
Consider an example in which several parties are fluent in various languages, but none of them speak the others' native language. However they all speak a little Esperanto. While they might get by with numerous translations of other languages, each language being understood by a few participants, Esperanto is the lowest common denominator.