Find the $\text{g.c.d.}$ and $\text{l.c.m.}$ of $510$ and $92$ using the fundamental theorem of arithmetic.

(N/A) Step $1$: Find the prime factorization of the given numbers.
$510 = 2 \times 3 \times 5 \times 17$
$92 = 2^2 \times 23$
Step $2$: To find the $\text{g.c.d.}$,take the product of the smallest power of each common prime factor.
$\text{g.c.d.} (510, 92) = 2^1 = 2$
Step $3$: To find the $\text{l.c.m.}$,take the product of the highest power of each prime factor involved.
$\text{l.c.m.} (510, 92) = 2^2 \times 3^1 \times 5^1 \times 17^1 \times 23^1 = 4 \times 3 \times 5 \times 17 \times 23 = 23460$