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Ratio of LCM & GCF | Algebra | AMC 8, 2013 | Problem 10

Try this beautiful problem from Algebra based on the ratio of LCM & GCF from AMC-8, 2013.

Ratio of LCM & GCF | AMC-8, 2013 | Problem 10

What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?

  • 310
  • 330
  • 360

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AMC-8, 2013 problem 10

Challenges and Thrills in Pre College Mathematics

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We have to find out the ratio of least common multiple and greatest common factor of 180 and 594. So at first, we have to find out prime factors of 180 & 594. Now.......

\(180=3^2\times 5 \times 2^2\)

\(594=3^3 \times 11 \times 2\)

Can you now finish the problem ..........

Now lcm of two numbers i.e multiplications of the greatest power of all the numbersĀ 

Therefore LCM of 180 & 594=\(3^3\times2^2 \times 11 \times 5\)=\(5940\)

For the GCF of 180 and 594, multiplications of the least power of all of the numbers i.e \(3^2\times 2\)=\(18\)

can you finish the problem........

Therefore the ratio of Lcm & gcf of 180 and 594 =\(\frac{5940}{18}\)=\(330\)

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