Question 2
Exercise 14. For any two numbers $x$ and $y$, their LCM and GCD are related by the following formula:
$$\operatorname{GCD}(x,y)\times\operatorname{LCM}(x,y)=xy.$$
Given that the product of two numbers is 3240 and their GCD is $2\times3^2$, find the LCM in index notation.
**Editorial input convention:** Take x and y to be positive integers. Enter prime powers in increasing prime order, using ^ for powers and * for multiplication, no spaces; omit exponent 1. Format example, not the answer: 2^3*7.
$$\operatorname{GCD}(x,y)\times\operatorname{LCM}(x,y)=xy.$$
Given that the product of two numbers is 3240 and their GCD is $2\times3^2$, find the LCM in index notation.
**Editorial input convention:** Take x and y to be positive integers. Enter prime powers in increasing prime order, using ^ for powers and * for multiplication, no spaces; omit exponent 1. Format example, not the answer: 2^3*7.