To rename the fractions 5/12 and 7/8 using the least common denominator, we first need to find the least common denominator (LCD) of 12 and 8.
1. **Find the LCD:**
- The prime factors of 12 are 2² * 3.
- The prime factors of 8 are 2³.
The LCD is the highest power of each prime number that appears in the factorizations:
- For 2: the highest power is 2³.
- For 3: the highest power is 3¹.
So, the LCD of 12 and 8 is 2³ * 3 = 8 * 3 = 24.
2. **Convert each fraction to have the LCD as the denominator:**
- For 5/12:
\[
\frac{5}{12} \times \frac{2}{2} = \frac{10}{24}
\]
- For 7/8:
\[
\frac{7}{8} \times \frac{3}{3} = \frac{21}{24}
\]
So, the fractions 5/12 and 7/8 renamed using the least common denominator of 24 are 10/24 and 21/24, respectively.
