Find the least common multiple (LCM) of $9$ and $12$ using the Prime Factors Method. Step 1. Write the prime factorization for each number: $9 = 3 \cdot 3$ and $12 = 2 \cdot 2 \cdot 3$. Step 2. Align matching prime factors vertically: $9 = \quad \quad 3 \cdot 3$ $12 = 2 \cdot 2 \cdot 3$ Step 3. Bring down one number from each column: $2$, $2$, $3$, and $3$. Step 4. Multiply the resulting factors to find the LCM: $ext{LCM} = 2 \cdot 2 \cdot 3 \cdot 3 = 36$. The least common multiple of $9$ and $12$ is $36$.