Final answer:
The least common denominator of 1/7 and 2/3 is found by multiplying the denominators 7 and 3 together, resulting in 21 as the least common denominator.
Step-by-step explanation:
To find the least common denominator (LCD) of 1/7 and 2/3, we need to find the smallest number that is a multiple of both denominators, which are 7 and 3. In this case, neither denominator is a multiple of the other, so we find the LCD by multiplying the two denominators together.
The calculation would look like this:
So, the least common denominator for the fractions 1/7 and 2/3 is 21, which is option c.