Question 124
Suppose we denote by $n_{(10)}$ the decimal representation for a positive integer $n$. Suppose three distinct positive integers $a, b, c$ satisfy all of the following conditions:
* $c_{(10)}$ coincides with the number obtained by removing a 6 from $a_{(10)}$.
* $c_{(10)}$ coincides with the number obtained by removing a 6 from $b_{(10)}$.
* The number of digits for $a$ coincides with the number of digits for $b$, and $a$ is a multiple of $b$.
Determine the smallest possible value that $c$ can have satisfying these conditions.
* $c_{(10)}$ coincides with the number obtained by removing a 6 from $a_{(10)}$.
* $c_{(10)}$ coincides with the number obtained by removing a 6 from $b_{(10)}$.
* The number of digits for $a$ coincides with the number of digits for $b$, and $a$ is a multiple of $b$.
Determine the smallest possible value that $c$ can have satisfying these conditions.