Find the $\text{g.c.d.}$ and $\text{l.c.m.}$ of $12$,$15$,and $21$ using the fundamental theorem of arithmetic.

(N/A) To find the $\text{g.c.d.}$ and $\text{l.c.m.}$ using the fundamental theorem of arithmetic,we first find the prime factorization of each number:
$12 = 2^2 \times 3^1$
$15 = 3^1 \times 5^1$
$21 = 3^1 \times 7^1$
The $\text{g.c.d.}$ is the product of the smallest power of each common prime factor:
$\text{g.c.d.}(12, 15, 21) = 3^1 = 3$
The $\text{l.c.m.}$ is the product of the highest power of each prime factor involved:
$\text{l.c.m.}(12, 15, 21) = 2^2 \times 3^1 \times 5^1 \times 7^1 = 4 \times 3 \times 5 \times 7 = 420$
Thus,the $\text{g.c.d.}$ is $3$ and the $\text{l.c.m.}$ is $420$.