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

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 =\(\frac{5940}{18}\)=\(330\)