Let, the two consecutive even numbers are x and (x+2) respectively, then x(x+2)=582168 ⇒x2+2x–582168=0 ⇒x2+764x–762x–582168=0 ⇒x(x+764)–762(x+764)=0 ⇒(x–762)(x+764)=9 Hence, x=762 or, x=–764 (Impossible) Thus, smaller number = 762