The correct answer is option (D):
168
The problem asks us to find the least number of students that can be arranged in rows of 8, 12, or 14. This means the number of students must be a multiple of 8, 12, and 14. To find the smallest such number, we need to find the least common multiple (LCM) of 8, 12, and 14.
Let's find the prime factorization of each number:
* 8 = 2 x 2 x 2 = 2^3
* 12 = 2 x 2 x 3 = 2^2 x 3
* 14 = 2 x 7
To find the LCM, we take the highest power of each prime factor present in any of the factorizations:
* The highest power of 2 is 2^3 = 8
* The highest power of 3 is 3^1 = 3
* The highest power of 7 is 7^1 = 7
Now, multiply these highest powers together: 8 x 3 x 7 = 168
Therefore, the least number of students in the class is 168. This means the correct answer is 168, as 168 is divisible by 8, 12, and 14.