anonymous
  • 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
katieb
  • katieb
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

jagatuba
  • jagatuba
I don't think you are missing anything. The GCD of 18=18 and the LCM of 540=540, so as far as the problem goes with the figures you are given the theorem holds true.
anonymous
  • anonymous
Thank you.
mathmate
  • mathmate
It is probably a trick question, because it asked "Which pairS of integers a and b ..." implies that you need to find ALL the pairs. Your logic is perfectly accurate, so let's continue from there. Break 540 into factors \( 540=(3^2.2).3.2.5 = 18.3.2.5\) So the pairs of A and B could be taken from the set \(S=\{18,1,3,2,5\} \) such that \(A \cup B = S \ and\ A \cap B = \{18\}\) From this, we can find pairs of a,b such as (18,540), (36,270),(54,180),(90,108), all satisfying the above conditions.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.