Henry Ernest Dudeney/Modern Puzzles/67 - A Digital Difficulty

by : $67$

 * A Digital Difficulty
 * Arrange the $10$ digits, $1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 \ 0$, in such order that they shall form a number
 * that may be divided by every number from $2$ to $18$ without in any case a remainder.


 * ''As an example, if I arrange them thus, $1 \ 2 \ 7 \ 4 \ 9 \ 5 \ 3 \ 6 \ 8 \ 0$, this number can be divided by $2$, $3$, $4$, $5$ and so on up to $16$, without any remainder,'
 * but it breaks down at $17$.