To find a common denominator for the fractions \( \frac{1}{2} \) and \( \frac{2}{7} \), we need to find the least common multiple (LCM) of the denominators 2 and 7.
The multiples of 2 are:
- 2, 4, 6, 8, 10, 12, 14, 16, ...
The multiples of 7 are:
- 7, 14, 21, 28, ...
The smallest common multiple is 14.
Thus, the common denominator for \( \frac{1}{2} \) and \( \frac{2}{7} \) is 14.