jmc

The numbers $a_1,$ $a_2,$ $a_3,$ $b_1,$ $b_2,$ $b_3,$ $c_1,$ $c_2,$ $c_3$ are equal to the numbers $1,$ $2,$ $3,$ $\dots ,$ $9$ in some order. Find the smallest possible value of $$a_1{a}_2{a}_3+b_1{b}_2{b}_3+c_1{c}_2{c}_3.$$