2001 AIME I Problem 12

A sphere is inscribed in the tetrahedron whose vertices are A = (6,0,0), B = (0,4,0), C = (0,0,2), and D = (0,0,0). The radius of the sphere is m/n, where m and n are relatively prime positive integers. Find m + n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.