Question 6
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 note for this self-study exercise:** x and y are positive integers. Enter the prime-factor index form with increasing prime bases, ^ for powers, * for multiplication, no spaces, and omit exponent 1. Format-only example: `2^3*7^2*11`.
$\operatorname{GCD}(x,y)\times\operatorname{LCM}(x,y)=xy$.
Given that the product of two numbers is 3240 and their GCD is $2\times3^2$, find the LCM in index notation.
**Editorial note for this self-study exercise:** x and y are positive integers. Enter the prime-factor index form with increasing prime bases, ^ for powers, * for multiplication, no spaces, and omit exponent 1. Format-only example: `2^3*7^2*11`.