jmc

To find either the LCM or the GCF of two numbers, always prime factorize first. The prime factorization of $180=3^2\times 5\times 2^2$. The prime factorization of $594=3^3\times 11\times 2$. Then, to find the LCM, we have to find the greatest power of all the numbers there are; if one number is one but not the other, use it (this is $3^3,5,11,2^2$). Multiply all of these to get 5940. For the GCF of 180 and 594, use the least power of all of the numbers that are in both factorizations and multiply. $3^2\times 2$ = 18. Thus the answer = $\frac{5940}{18}$ = $\boxed{330}$.