To determine the least common denominator (LCD) for the fractions [tex]\( \frac{1}{3}, \frac{3}{4}, \frac{5}{32}, \frac{1}{9} \)[/tex], we need to follow these steps:
1. Identify the Denominators:
The denominators of the fractions are 3, 4, 32, and 9.
2. Find the Least Common Multiple (LCM) of the Denominators:
- First, find the LCM of the first two denominators, 3 and 4.
- The LCM of 3 and 4 is 12.
- Next, find the LCM of this result (12) with the next denominator, which is 32.
- The LCM of 12 and 32 is 96.
- Finally, find the LCM of this result (96) with the last denominator, which is 9.
- The LCM of 96 and 9 is 288.
Therefore, the least common denominator for the fractions [tex]\( \frac{1}{3}, \frac{3}{4}, \frac{5}{32}, \frac{1}{9} \)[/tex] is 288.
The correct answer is:
D. 288
