What is the least common multiple of 9, 17, and 51? A. 51 B. 102 C. 153 D. 867

The least common multiple (LCM) of 9, 17, and 51 can be found by first identifying the prime factors of each number.

1. The prime factors of 9 are 3 and 3.
2. The prime factors of 17 are 17.
3. The prime factors of 51 are 3 and 17.

Next, for each prime number, we take the highest power that appears in the factorization of either number.

1. The highest power of 3 that appears is 3^2 (from the number 9).
2. The highest power of 17 that appears is 17^1 (from the numbers 17 and 51).

Finally, we multiply these highest powers together to get the LCM.

LCM = 3^2 * 17^1 = 9 * 17 = 153

So, the least common multiple of 9, 17, and 51 is 153. Therefore, the answer is C. 153.