To determine the least common multiple (LCM) and thus the least common denominator for the fractions [tex]\( \frac{2}{3}, \frac{5}{6}, \frac{9}{4} \)[/tex], we need to follow these steps:
1. Identify the denominators of the given fractions. The denominators are 3, 6, and 4.
2. Find the LCM of the first two denominators (3 and 6). The LCM of 3 and 6 is 6 because 6 is the smallest number that 3 and 6 both divide evenly into.
3. Now, find the LCM of the result (which is 6) and the third denominator (4). The LCM of 6 and 4 is 12 because 12 is the smallest number that both 6 and 4 divide evenly into.
Thus, the least common multiple (LCM) and the least common denominator for the fractions [tex]\( \frac{2}{3}, \frac{5}{6}, \frac{9}{4} \)[/tex] is 12.
So, the best answer is:
B. 12
