\(\overline{abc}\times126=\overline{15abc}\)
\(\Leftrightarrow\overline{abc}\times126=15000+\overline{abc}\)
\(\Leftrightarrow\overline{abc}\times\left(126-1\right)=15000\)
\(\Leftrightarrow\overline{abc}\times125=15000\)
\(\Rightarrow\overline{abc}=15000\div125=120\)