Questions: The least common denominator for 6/10, 5/8, 3/4, and 1/2 is - 32. - 40. - 80. - 12.

Transcript text: The least common denominator for $\frac{6}{10}, \frac{5}{8}, \frac{3}{4}$, and $\frac{1}{2}$ is - 32. - 40. - 80. - 12.

Solution

Solution Steps

To find the least common denominator (LCD) of the fractions $\frac{6}{10}$, $\frac{5}{8}$, $\frac{3}{4}$, and $\frac{1}{2}$, we need to determine the least common multiple (LCM) of their denominators: 10, 8, 4, and 2. The LCM is the smallest number that is a multiple of each of these denominators.

Step 1: Identify the Denominators

The given fractions are $\frac{6}{10}$, $\frac{5}{8}$, $\frac{3}{4}$, and $\frac{1}{2}$. The denominators are 10, 8, 4, and 2.

Step 2: Find the Least Common Multiple (LCM)

To find the least common denominator, we need to calculate the least common multiple of the denominators 10, 8, 4, and 2. The LCM is the smallest number that is a multiple of each of these denominators.

Step 3: Calculate the LCM

The least common multiple of 10, 8, 4, and 2 is 40. This is because 40 is the smallest number that all these denominators divide into without leaving a remainder.