\(abc=ab+bc+ca\Rightarrow100a+10b+c=10a+b+10b+c+10c+a\)
\(\Rightarrow100a+10b+c=11a+11b+11c\)
\(\Rightarrow\left(100a-11a\right)=\left(11b-10b\right)+\left(11c-c\right)\)
\(\Rightarrow89a=b+10c\)
\(\Rightarrow a=1;b=9;c=8\)
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