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What is a common denominator for [tex]$\frac{6}{7}$[/tex] and [tex]$\frac{1}{6}$[/tex]?

A. 13
B. 36
C. 42
D. 49


Sagot :

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].
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