"They came to the same conclusion."
Translation:Ellos llegaron a la misma conclusión.
Venir means physically coming to a location, whereas llegar can mean "arrive" or "come" in the abstract sense as is the case in this sentence.
Well, alcanzar is "reach". In physical terms, it can mean to catch up with somebody or to extend your grasp to reach something. I'm not sure whether it can be used metaphorically like llegar, but if it can, it definitely seems like a possibility for this sentence.
Yes, it can be used with that meaning:
Alcanzar la sabiduría. Llegar a la cumbre del saber.
But 'Alcanzaron la misma conclusión' is not bad, but it sounds a little weird.
Why is "Ellos llegaron al mismo conclusión" no valid, does it have to be "la misma"?
Llegaron a la misma conclusion would also be correct, as the verb tells you it is third person plural