Productive numberLogic Level pending
Number \(M\) has the following characteristics:
- All the digits of \(M\) are different.
- The product of any two adjacent digits in \(M\) is also a number included in \(M\).
For example: 241836 satisfies the two conditions because the products of \(2\times 4=8\), \(4\times 1=4\), \(1\times 8=8\), \(8\times 3=24\), and \(3 \times 6=18\) are found in \(M\).
Find the largest of such number \(M\).