Successive Digit Division

Find the largest integer N,
such that the number made of the first k digits is divisible by k, for
k=1,2,3,...,n, with n equal to the number of digits in N. (Solve for n
from 1 to 15.)

Repeat, finding the smallest positive integer N in each case.
Some sites with divisibility tests:
Source: Philippe Fondanaiche. Similar to a
previous
puzzle. It was pointed out to me that this was the same puzzle as
used on
IBM's Ponder This.
Solution
Mail to Ken