Which number is a common denominator for \( \frac{1}{6} \) and \( \frac{3}{5} \) \begin{tabular}{|c|c|c|c|}\hline 3 & 4 & 11 & 30 \\ \hline\end{tabular}

To find a common denominator for \( \frac{1}{6} \) and \( \frac{3}{5} \), we need the least common multiple (LCM) of 6 and 5. The LCM of 6 (which factors to \( 2 \times 3 \)) and 5 (which is prime) is calculated by taking the highest power of each prime that appears in the factorization. Thus, we get \( LCM(6, 5) = 2^1 \times 3^1 \times 5^1 = 30 \). So, the common denominator is 30! Both fractions can be converted into the same denominator of 30: \( \frac{1}{6} = \frac{5}{30} \) and \( \frac{3}{5} = \frac{18}{30} \). Thus, the answer from the choices given is 30. Isn’t math just like a puzzle? You get to figure out how different pieces fit together! Keeping those prime factors in mind can help you tackle all sorts of fraction challenges. When working with fractions, a common mistake is forgetting to multiply both the numerator and denominator when adjusting the denominator. So when changing to 30, make sure you're scaling properly to keep everything balanced!