The least common multiple (LCM) of 9, 11, and 12 is 1188.
To find the LCM, we first need to determine the prime factors of each number:
- 9 = 3 × 3 = 3²
- 11 = 11 (11 is a prime number)
- 12 = 2 × 2 × 3 = 2² × 3
Next, we take the highest power of each prime factor that appears in any of the numbers:
- For the prime number 2, the highest power is 2² (from 12).
- For the prime number 3, the highest power is 3² (from 9).
- For the prime number 11, the highest power is 11 (from 11).
Now we multiply these together to find the LCM:
LCM = 2² × 3² × 11 = 4 × 9 × 11 = 36 × 11 = 396.
So, the least common multiple of 9, 11, and 12 is 396.