Four mathematicians, none yet a centenarian, meet for coffee. The graph-theorist among them noticed that the common divisor graph of their ages (that is, the graph whose vertices are their ages, two of which are joined by an edge if, and only if, they have a common divisor greater than 1) is the simple square (left below).

After some thought, the number-theorist observed that if the Collatz recipe (multiply by 3, and add 1 if odd; divide by 2 if even) were applied to each of their ages, the resulting common divisor graph of the four numbers would be the star (right).

How old is Freddy, the youngest of the mathematicians?