9. (10 points) In a six-digit number, any 3 consecutive digits form a three-digit number that is divisible by 6 or 7. The smallest six-digit number is $\qquad$

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【Analysis】Since any 3 consecutive arrangements are three-digit numbers, it indicates that there is no 0 in this six-digit number. To make the six-digit number the smallest, we might as well assume that the six-digit number is $11 \square \square \square \square$, and solve the problem using the method of case analysis.

【Solution】Solution: Since any 3 consecutive arrangements are three-digit numbers, it indicates that there is no 0 in this six-digit number.
To make the six-digit number the smallest, we might as well assume that the six-digit number is $11 \square \square \square \square$,
(1)
11q0םव
$11 x$
(2) $\qquad$
(3)
(4) $\qquad$
(1) $11 x$, then we have $\left\{\begin{array}{ll}11 \mathrm{x} \div 6=19 & 19 \times 6=114 \\ 11 \mathrm{x} \div 7=16 & 16 \times 7=114 \text { (smallest) }\end{array}\right\} \Rightarrow(1112$,
(2) $12 X$, then we have $\left\{\begin{array}{ll}12 \mathrm{x} \div 6=21 & 21 \times 6=126 \\ 12 \mathrm{x} \div 7=18 & 18 \times 7=126\end{array}\right) \Rightarrow$ (2) 126 ,
(4) $64 x$, then we have $\left\{\begin{array}{ll}64 \mathrm{x} \div 6=107 & 107 \times 6=642 \text { (smallest) } \\ 64 \mathrm{x} \div 7=92 & 92 \times 7=644\end{array}\right\} \Rightarrow 44642$,

Therefore, the answer is 112642