Let u,v ∈ \ {0} define A as A={a∈ N\{0} : u|a and v|a}

I want to prove two things

1) I want to show that A has a smallest element and call this b

2) Show that for every a∈ A follows b|a

1) I know that a fundamental follow of the axiom of induction is that every not empty subset of N contains a smallest element.

I need to show that A is a not empty subset. ( I don't know how to do this because I have no questions or explanation in my math book )