To determine the least common denominator (LCD) for the two fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex], we need to find the least common multiple (LCM) of their denominators, 4 and 6.
Here are the detailed steps:
1. List the multiples of each denominator:
- Multiples of 4: [tex]\(4, 8, 12, 16, 20, 24, \ldots\)[/tex]
- Multiples of 6: [tex]\(6, 12, 18, 24, 30, \ldots\)[/tex]
2. Identify the smallest common multiple from these lists:
- As we can observe, the smallest common multiple of both 4 and 6 is 12.
Thus, the least common multiple of 4 and 6 is 12, which means the least common denominator for the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] is 12.
So, the correct answer is:
[tex]\[
\boxed{12}
\][/tex]
