PE-MO 2011 Problem 1

We say that a positive integer is irregular if said number is not a multiple of none of its digits. For example, $203$ is irregular because $203$ is not a multiple of $2$ , it is not multiple of $0$ and is not a multiple of $3$ . Consider a set consisting of $n$ consecutive positive integers. If all the numbers in that set are irregular, determine the largest possible value of $n$ .