Is this a trick question?
"Which pairs of integers \(a\) and \(b\) have greatest common divisor \(18\) and least common multiple \(540\)?"
There is a theorem that states that \([a,b](a,b)=ab\), where \([a,b]\) stands for the least common multiple of \(a\) and \(b\), and \((a,b)\) stands for the greatest common divisor of \(a\) and \(b\).
So, it follows that\[[a,b](a,b)=ab,\]\[540\cdot18=a\cdot b.\]In other words, \(a=540\) and \(b=18\) would suffice.
Am I missing something?

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