Try this beautiful problem from Algebra based on the ratio of LCM & GCF from AMC-8, 2013.
What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?
Algebra
Ratio
LCM & GCF
Answer:$330$
AMC-8, 2013 problem 10
Challenges and Thrills in Pre College Mathematics
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 numbers
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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