NKJV - 26 Then Paul took the men, and the next day, having been purified with them, entered the temple to announce the expiration of the days of purification, at which time an offering should be made for each one of them.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
It's possible, since we know they were in Jerusalem, and that ALL the elders were present at that time...
That the specific purification was as prescribed for the "Day of Atonement.'
If this theory is correct then the purification would be very similar to that described in: