Riddle in a life span

Little is known about the life of Diophantus (we know he lived sometime between 100 and 400 A.D.), the Greek father of algebra, except his age at the time of his death, which has been preserved in the famous 1,500-year-old riddle given below.  The Riddle divides Diophantus’ life into segments, each of which is a part of his total age.

The riddle is:

Diophantus’ youth lasted 1/6 of his life.  He grew a beard after 1/12 more.  After 1/7 more of his life, Diophantus married; five years later, he had a son.  The son lived exactly 1/2 as long as his father, and Diophantus died just four years after his son.  All of this adds up to the years Diophantus lived.

How old was Diophantus at his death?