marine biologists have been studying newly discovered species of fish. Each type is found in a certain group size. The scientists are investigating similarities of gro including the lowest common group number (lowest common multiple). \begin{tabular}{l|l} oups of 12 & \\ \hline oups of seven & \\ \hline\end{tabular}

It looks like you're investigating the group sizes of newly discovered fish species and aiming to find the **Lowest Common Multiple (LCM)** of these group sizes. Based on your table, you have two group sizes: - **Groups of 12** - **Groups of 7** ### Understanding the Problem The **Lowest Common Multiple (LCM)** of two numbers is the smallest number that is a multiple of both numbers. In this context, finding the LCM of 12 and 7 will help determine the smallest group size that accommodates both species' grouping patterns simultaneously. ### Calculating the LCM of 12 and 7 1. **Prime Factorization**: - **12**: \( 2^2 \times 3 \) - **7**: \( 7 \) (since 7 is a prime number) 2. **Identify Common and Unique Factors**: - There are no common prime factors between 12 and 7. 3. **Calculate the LCM**: - Multiply the highest powers of all prime factors present in both numbers. - \( \text{LCM} = 2^2 \times 3 \times 7 = 4 \times 3 \times 7 = 84 \) ### Conclusion The **Lowest Common Multiple (LCM)** of **12** and **7** is **84**. This means that a group size of **84** is the smallest number that is a multiple of both **12** and **7**. In the context of your marine biology study, this could indicate that after every 84 individuals, the grouping patterns of both species align. ### Updated Table Here's the completed table with the LCM included: \[ \begin{tabular}{|l|l|} \hline \textbf{Group Size} & \textbf{Details} \\ \hline Groups of 12 & \\ \hline Groups of 7 & \\ \hline \textbf{LCM} & 84 \\ \hline \end{tabular} \] If you have more group sizes or additional details you'd like to analyze, feel free to share!