Find the LCM of Denominators: 3, 9, and 12

To find the least common multiple (LCM) of $3$, $9$, and $12$, begin by finding their prime factorizations:

$3 = 3$

$9 = 3^2$

$12 = 2^2 \, \times \, 3$

The LCM is calculated by taking the highest power of each prime present:

Max of $2$ is $2^2$ and of $3$ is $3^2$.

Thus, LCM is $2^2 \, \times \, 3^2 = 4 \, \times \, 9 = 36$.