What is luca and how long ago did luca exist? what is the general interpretation of the observation that members of a single gene family are found in all three domains of life?

LUCA the last universal common ancestor; it is exist  in 3.5 billon years ago in the paleoarchean era, a few hundred million years after the earlier fossils evidence of life.

Explanation:

It is the single celled bacteria like organisms living in volcanic era. The three domain of the life are Archaea, bacteria, Eukaryotas. The observation that member of the single gene family are found in the all three domain of life.

It is suggested that the progenitor gene that give rise to the family member existed in the LUCA , before the time that the three domain diverged.