If $a\oplus b=\text{L.C.M. of }a\text{ and }b$, and $a\otimes b=\text{G.C.F. of }a\text{ and }b$, then find the value of:
$$(12\otimes 16)\oplus (24\otimes 36)$$

Let's compute the values step-by-step using the given definitions:
1. Evaluate the first term $(12\otimes 16)$, which represents the Greatest Common Factor ($\text{G.C.F.}$) of $12$ and $16$:

$$12\otimes 16=\text{G.C.F.}(12,16)=4$$

2. Evaluate the second term $(24\otimes 36)$, which represents the Greatest Common Factor ($\text{G.C.F.}$) of $24$ and $36$:

$$24\otimes 36=\text{G.C.F.}(24,36)=12$$

3. Now, substitute these values into the full expression and apply the $\oplus$ operator, which represents the Least Common Multiple ($\text{L.C.M.}$):

$$4\oplus 12=\text{L.C.M.}(4,12)=12$$