• anonymous
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?
Mathematics

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