To find the lowest common multiple (LCM) of the denominators of the fractions $\frac{118}{118}$ and $\frac{827}{827}$, we first need to identify the denominators.

However, it seems like the fractions $\frac{118118}{?}$ and $\frac{827827}{?}$ might be mistyped, because they repeat the numerator. Assuming you meant two fractions that have denominators 118 and 827, the question should focus on the LCM of these denominators.

Here are the steps to find the LCM:

1. Denominators:

   • First denominator: $118$
   • Second denominator: $827$

2. Prime factorization:

   • $118 = 2 \times 59$ (where 59 is a prime number)
   • $827 = 827$ (since 827 is a prime number)

3. LCM Calculation:
   Since 118 and 827 have no common factors, the LCM is their product: $\text{LCM} = 118 \times 827 = 97586$

This is not matching the options provided, so let's correct this by re-interpreting that the denominators might have been intended as powers of 3 and 9. Please clarify if I should solve these factors correctly or verify options.

Would you like more details or assistance with another interpretation of the problem?