1. **State the problem:** Find the least common multiple (LCM) of the numbers 3, 9, and 12. 2. **Recall the formula and rules:** The LCM of a set of numbers is the smallest positive integer that is divisible by all of them. 3. **Find prime factorizations:** - $3 = 3$ - $9 = 3^2$ - $12 = 2^2 \times 3$ 4. **Determine the highest powers of each prime:** - For prime 2: highest power is $2^2$ (from 12) - For prime 3: highest power is $3^2$ (from 9) 5. **Calculate the LCM:** $$\text{LCM} = 2^2 \times 3^2 = 4 \times 9 = 36$$ 6. **Final answer:** The least common multiple of 3, 9, and 12 is **36**.