Question 2
Alice chooses positive integers $a,b,c$. There is exactly one ordered triple of positive integers $(x,y,z)$ satisfying $a=\operatorname{lcm}(x,y)$, $b=\operatorname{lcm}(x,z)$, $c=\operatorname{lcm}(y,z)$. She tells Bob that the triple exists uniquely and gives him $a,b$. Prove that Bob can determine $c$.