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AMC 8 Math Olympiad USA Math Olympiad

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

Try this beautiful problem from Algebra aboutRatio of Lcm & gcf from AMC-8, 2013. You may use sequential hints to solve the problem.

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

Key Concepts


Algebra

Ratio

LCM & GCF

Check the Answer


Answer:$330$

AMC-8, 2013 problem 10

Challenges and Thrills in Pre College Mathematics

Try with Hints


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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