To determine the least common denominator (LCD) of the fractions [tex]\(\frac{3}{4}\)[/tex], [tex]\(\frac{4}{5}\)[/tex], and [tex]\(\frac{2}{3}\)[/tex], we need to find the least common multiple (LCM) of their denominators.
Here are the denominators of the given fractions:
- Denominator 1: 4
- Denominator 2: 5
- Denominator 3: 3
The first step is to find the LCM of these three numbers.
1. LCM of 4 and 5:
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
- The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, ...
- The smallest common multiple is 20. So, the LCM of 4 and 5 is 20.
2. LCM of 20 and 3:
- The multiples of 20 are: 20, 40, 60, 80, 100, ...
- The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, ...
- The smallest common multiple of 20 and 3 is 60. So, the LCM of 20 and 3 is 60.
Thus, the least common denominator of [tex]\(\frac{3}{4}\)[/tex], [tex]\(\frac{4}{5}\)[/tex], and [tex]\(\frac{2}{3}\)[/tex] is [tex]\(60\)[/tex].
So, the correct answer is:
B. [tex]\(60\)[/tex]
