To find the Least Common Denominator (LCD) for the fractions [tex]\( \frac{1}{3}, \frac{3}{4}, \frac{5}{32}, \)[/tex] and [tex]\( \frac{8}{9} \)[/tex], we follow these steps:
1. Identify the denominators of the given fractions: [tex]\(3\)[/tex], [tex]\(4\)[/tex], [tex]\(32\)[/tex], and [tex]\(9\)[/tex].
2. Find the Least Common Multiple (LCM) of these denominators. The LCM of a set of numbers is the smallest number that is a multiple of each of the numbers in the set.
The denominators are [tex]\(3\)[/tex], [tex]\(4\)[/tex], [tex]\(32\)[/tex], and [tex]\(9\)[/tex].
Following the proper calculations for LCM, the Least Common Denominator of these fractions is determined to be:
C. 288
Thus, the best answer is [tex]\( \boxed{288} \)[/tex].
