\(-\text{Theo bài ra: }\overline{abc}+\overline{bca}+\overline{cab}=666\)
\(\Rightarrow100a+10b+c+100b+10c+a+100c+10a+b=666\)
\(\Rightarrow111a+111b+111c=666\)
\(\Rightarrow111\left(a+b+c\right)=666\)
\(\Rightarrow a+b+c=6\)
\(-Do\left\{{}\begin{matrix}a>b>c>0\\a;b;c\in N\circledast\end{matrix}\right.\text{ nên suy ra }\left\{{}\begin{matrix}a=3\\b=2\\c=1\end{matrix}\right.\)
\(\text{Vậy số cần tìm là 321.}\)