The least common multiple (LCM) of 8, 9, and 11 is 792.
To understand how we arrive at this answer, we first need to find the prime factorization of each number:
- 8 = 2 × 2 × 2 = 23
- 9 = 3 × 3 = 32
- 11 = 111 (11 is a prime number)
Next, the LCM is found by taking the highest power of each prime that appears in the factorizations:
- For 2, the highest power is 23.
- For 3, the highest power is 32.
- For 11, the highest power is 111.
Now we can calculate the LCM:
LCM = 23 × 32 × 111 = 8 × 9 × 11 = 792.
Therefore, the least common multiple of 8, 9, and 11 is 792.