Teaser 2902: Birthdays 2018

From The Sunday Times, 6th May 2018 [link]

Several friends have birthdays on different days in 2018.

Replacing A by 1, B by 2, C by 3 … and Z by 26, each month and day can be replaced by a sequence of numbers. Every birthday is given numerically by day, date and month, as described above. For each friend, there is just one number common to each of their 3 sets of numbers. The number of friends is the largest possible.

How many friends are there and what is the largest number of clear days between consecutive birthdays?