Final answer:
The denominator that makes the fraction with the numerator of 6 in its lowest terms is 19, as it has no common factors with 6 except for 1.
Step-by-step explanation:
The question asks which of the given denominators would allow a fraction with a numerator of 6 to be in its lowest terms. A fraction is in its lowest terms when the numerator and the denominator have no common factors besides 1. To determine the correct answer, we must find the denominator that does not share any factors with 6, other than 1.
Now, let's analyze the options:
- A 9 (6 and 9 share a common factor of 3)
- B 12 (6 and 12 share a common factor of 6)
- C 15 (6 and 15 share a common factor of 3)
- D 18 (6 and 18 share a common factor of 6)
- E 19 (6 and 19 have no common factors other than 1)
Thus, the only suitable option where the fraction is already in its lowest terms is with the denominator 19.