To determine a common denominator for the fractions [tex]\(\frac{6}{7}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex], we need to find the least common multiple (LCM) of their denominators.
The denominators of the fractions are 7 and 6.
To find the LCM of 7 and 6, we list out the multiples of each number:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...
The smallest multiple that appears in both lists is 42. Therefore, the least common multiple of 7 and 6 is 42.
Thus, a common denominator for the fractions [tex]\(\frac{6}{7}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex] is [tex]\( \boxed{42} \)[/tex].
