Finding longest common substring among filenames

Shell Programming and Scripting
1

I will be performing a task on several directories, each containing a large number of files (2500+) that follow a regular naming convention:

YYYY_MM_DD_XX.foo_bar.A.B.some_different_stuff.EXT

What I would like to do is automatically discover the part of the filenames that are common to all 2500 files, so that a script could use that as a base name. In practice, this will end up being "YYYY_MM_DD_XX.foo_bar."

I figured out as far as I'll have to use ls to get all the filenames, but there's no command that I know of that will find the largest substring that exists among a large number of strings. I thought perhaps there would be some sed guru out there that would find this problem trivial. You sed experts always blow my mind.

2 
set -- *
files=$#
name=$1
while [ -n "$name" ]
do
  set -- $name*
  [ $# -eq $files ] && break
  name=${name%?}
done
echo $name