\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find all \((a, b) \in \mathbb{N}^* \times \mathbb{N}^*\) with \(a \leq b\), \(a \wedge b = 18\) and \(a \vee b = 540\). Hint. Set \(a = 18 a'\), \(b = 18 b'\) with \(a' \wedge b' = 1\).
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