Exactly the way you do it with numbers:
-- List all the factors of the first one.
-- List all the factors of the second one.
-- List all the factors of the third one.
-- Make a short list, consisting of the factors that appear
on all three lists. Those are the 'common' factors.
-- The greatest item on the short list is the greatest common factor.
14m², 27a³, and 45a² don't have any common factor except ' 1 '.
Since ' 1 ' is their only common factor, it's also their greatest one.