[tex]\it b:c=2 \Rightarrow b=2c\ \ \ \ \ (1)\\ \\ a:c=3 \Rightarrow a=3c\ \ \ \ \ \ (2)\\ \\ \\ a+b+c=12\ \stackrel{(1),(2)}{\Longrightarrow}\ \ 3c+2c+c=12 \Rightarrow 6c=12|_{:6} \Rightarrow c=2\\ \\ c=2\ \stackrel{(1)}{\Longrightarrow}\ b=2\cdot2=4\\ \\ c=2\ \stackrel{(2)}{\Longrightarrow}\ a=3\cdot2=6\\ \\ \overline{abc} =642[/tex]
