Sunday Times Teaser 3075 – Prime Cuts for Dinner
by Peter Good
Published Sunday August 29 2021 (link)
Tickets to the club dinner were sequentially numbered 1, 2, …, etc. and every ticket was sold. The number of guests for dinner was the highest common factor of three different two-figure numbers and the lowest common multiple of three different two-figure numbers. There were several dinner tables, each with the same number of seats, couples being seated with friends. The guests on each table added their ticket numbers together and obtained one of two prime numbers, both less than 150, but if I told you the larger prime number you would not be able to determine the other.
What was the larger of the two prime numbers?