To find 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 determine the least common multiple (LCM) of their denominators: 4, 5, and 3.
Step-by-Step Solution:
1. List the denominators:
- The denominators of the fractions are 4, 5, and 3.
2. Identify the prime factors of each denominator:
- The prime factorization of 4 is [tex]\( 2^2 \)[/tex].
- The prime factorization of 5 is [tex]\( 5^1 \)[/tex].
- The prime factorization of 3 is [tex]\( 3^1 \)[/tex].
3. Determine the highest power of each prime number present in the factorizations:
- The highest power of 2 in the factorizations is [tex]\( 2^2 \)[/tex].
- The highest power of 5 in the factorizations is [tex]\( 5^1 \)[/tex].
- The highest power of 3 in the factorizations is [tex]\( 3^1 \)[/tex].
4. Multiply these highest powers to find the LCM:
- LCM = [tex]\( 2^2 \times 5^1 \times 3^1 \)[/tex]
- LCM = 4 (which is [tex]\( 2^2 \)[/tex]) [tex]\( \times \)[/tex] 5 [tex]\( \times \)[/tex] 3
- LCM = 4 [tex]\( \times \)[/tex] 5 = 20
- 20 [tex]\( \times \)[/tex] 3 = 60
Thus, the least common denominator of [tex]\( \frac{3}{4} \)[/tex], [tex]\( \frac{4}{5} \)[/tex], and [tex]\( \frac{2}{3} \)[/tex] is 60.
Answer:
B. 60
