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
But try the problem first…
Answer:$330$
AMC-8, 2013 problem 10
Challenges and Thrills in Pre College Mathematics
Try with Hints
First hint
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 ……….
Second Hint
Now lcm of two numbers i.e multiplications of the greatest power of all the numbersÂ
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……..
Final Step
Therefore the ratio of Lcm & gcf of 180 and 594 =\(\frac{5940}{18}\)=\(330\)
Other useful links
- https://www.cheenta.com/perfect-cubes-algebra-amc-8-2018-problem-25/
- https://www.youtube.com/watch?v=LArf0rlglzk