Let $g$ and $l$ be given positive integers. Prove that integers $x$ and $y$ exist satisfying $(x,y)=g$ and $[x,y]=l$ if and only if $g|l$.
I am facing problem in proving the converse statement.
The converse statement is not clear to me. Are we supposed to prove the existence (The existence of $x$ and $y$ having the property $(x,y)=g$ and $[x,y]=l$) OR property (the existence of $x$ and $y$ is known and now need to prove that they satisfy the property $(x,y)=g $ and $[x,y]=l $ )