# Productive number

Logic Level pending

Number $$M$$ has the following characteristics:

1. All the digits of $$M$$ are different.
2. 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 $$M$$.

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