\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A, B \in \mathbb{K}[X]^*\) with \(A\) and \(B\) both monic. Show that \(A \vee B\) divides \(A B\), and that \(A \vee B = A B\) iff \(A \wedge B = 1\).
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