IKMC 2011 - Grades 11-12 - Paper 01 - Self-study Question 26

Different letters stand for distinct nonzero digits, and repeated letters have the same digit. What is the smallest positive integer value of $\dfrac{K\cdot A\cdot N\cdot G\cdot A\cdot R\cdot O\cdot O}{G\cdot A\cdot M\cdot E}$?