$(15$ points$)$ The Euclidean Algorithm is used to find the Greatest Common Divisor $($GCD$)$ of two positive numbers; i$.$e$.,$ GCD$(10,15)=5,$ as $10=25$ and $15=35,$ where $5$ is a $($and only in this case$)$ common divisor between $10$ and $10$; and since $5$ is the largest such divisor, it is the GCD$.$

Below are the steps of the algorithm for computing GCD:

$($i$)$ We put the larger number into R$1$ and the other number into R$2.$

$($ii$)$ Keep subtracting R$2$ from R$1,$ until R$1$ contains a smaller value than R$2$ does.

$($iii$)$ From Step $($ii$),$ if R$1$ contains a positive number, we exchange values in R$1$ and R$2,$ and repeat Step $($ii$).$

$($iv$)$ From Step $($ii$),$ if R$1$ contains a zero, we stop the program. What$$s in R$2$ is now the GCD$.$

Write an LC$-3$ assembly language program that implements the Euclidean Algorithm. $[$Hint: Might have additional steps in between; utilize CC for comparisons.$]$

Example: GCD$(624,36)[$i$.$e$.,$ R$1=624$ and R$2=36]=$ GCD$(588,36)=$ GCD$(552,36)=...$

$=$ GCD$(48,36)=$ GCD$(12,36)=$ GCD$(36,12)=$ GCD$(24,12)=$ GCD$(12,12)=$ GCD$(0,12)=12.$