The Kruger National Park is famous for its diverse wildlife. It is home to various species, including lions, zebras, and elephants. The park management wants to organise a special safari tour for visitors, where they can see each animal species in equal numbers. They have 24 lions, 36 zebras, and 48 elephants available for the safari tour. The park management wants to know the minimum number of safari tours they need to organise so that each animal species has an equal number of individuals and there are no animals left out. What is the minimum number of safari tours they need to organise to meet these requirements?

To determine the minimum number of safari tours the park management needs to organize so that each animal species has an equal number of individuals and there are no animals left out, we need to find the greatest common divisor (GCD) of the numbers of each species: 24 lions, 36 zebras, and 48 elephants.

### Steps to solve:

1. **List the factors of each number**:
   - Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
   - Factors of 36: \(1, 2, 3, 4, 6, 9, 12, 18, 36\)
   - Factors of 48: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\)

2. **Identify the greatest common factor (GCD)**:
   - Common factors: \(1, 2, 3, 4, 6, 12\)
   - The greatest common factor is 12.

3. **Determine the number of tours**:
   - Divide the number of each species by the GCD:
     - Lions: \(\frac{24}{12} = 2\)
     - Zebras: \(\frac{36}{12} = 3\)
     - Elephants: \(\frac{48}{12} = 4\)

   - Therefore, in each safari tour, there would be 2 lions, 3 zebras, and 4 elephants.

   - Since the GCD is 12, they need to organize **12 safari tours** to meet the requirement that each tour has an equal number of each species and no animals are left out.

### Conclusion:
The minimum number of safari tours the park management needs to organize is **12**.

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Would you like more details or have any questions? Here are some related questions:

1. What is the significance of the greatest common divisor in this context?
2. How would the solution change if the number of zebras was different?
3. What if the number of animals wasn't divisible by their GCD? How would that affect the tours?
4. Could we organize the animals in a different way to achieve the same goal?
5. How can the park management ensure that the tours are balanced over time?
6. What are some other scenarios where calculating the GCD is useful?
7. How do different methods for finding the GCD (like Euclidean algorithm) work?
8. How would you organize the tours if there were an odd number of one species?

**Tip:** Understanding the concept of GCD can help simplify a wide range of mathematical problems, particularly those involving distribution or allocation.

Discover how to calculate the minimum number of safari tours required for equal distribution of lions, zebras, and elephants in Kruger National Park. Learn about factors, greatest common divisor (GCD), and how to ensure each tour is balanced with no animals left out.

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