[Amankris]

2. The greatest common divisor of four positive integers, not necessarily distinct, is equal to 1. Their least common multiple is equal to their sum. Find the number of possible values of the sum of these four numbers.

G u i d e

ให้จำนวนทั้งสี่คือ $a,b,c,d$ และ $lcm[a,b,c,d]=ax=by=cz=dw$

จะได้ว่า $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}+\dfrac{1}{w}=1$