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

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To find the lowest common multiple (LCM) of the group sizes 12 and 7, we can follow these steps:

1. **Identify the prime factors of each number:**
   - The prime factorization of 12 is $$2^2 \times 3^1$$.
   - The prime factorization of 7 is $$7^1$$ (since 7 is a prime number).

2. **Determine the LCM:**
   - The LCM is found by taking the highest power of each prime factor that appears in the factorizations.
   - For 12, we have $$2^2$$ and $$3^1$$.
   - For 7, we have $$7^1$$.
   - Therefore, the LCM will be $$2^2 \times 3^1 \times 7^1$$.

3. **Calculate the LCM:**
   - First, calculate $$2^2 = 4$$.
   - Next, calculate $$3^1 = 3$$.
   - Then, calculate $$7^1 = 7$$.
   - Now, multiply these together: 
     $$
     LCM = 4 \times 3 \times 7
     $$

Let's perform the multiplication step by step:

- First, calculate $$4 \times 3 = 12$$.
- Then, calculate $$12 \times 7 = 84$$.

Thus, the lowest common multiple of 12 and 7 is $$84$$.

Therefore, the answer is:

$$
\text{LCM}(12, 7) = 84
$$
The lowest common multiple of 12 and 7 is 84.

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