The question in the image asks:

To support those impacted by the earthquake, an organization collected 324 kg of wheat, 81 liters of oil, and 108 kg of dal. They want to share each item equally among the families, ensuring that nothing is left over.

Task:
Find the maximum number of families that can receive equal shares of the three food items. (Note: The quantities of the three items being shared have to be in whole numbers.)

Solution:

To find the maximum number of families, we need to determine how many equal shares can be made such that each family gets a whole number of wheat, oil, and dal, and nothing is left over. This means we need to find the greatest common divisor (GCD) of the quantities of wheat (324 kg), oil (81 liters), and dal (108 kg).

1. Wheat: 324 kg
2. Oil: 81 liters
3. Dal: 108 kg

We will calculate the GCD of these three numbers: $\text{GCD}(324, 81, 108)$.

1. First, find the GCD of 324 and 81: $\text{GCD}(324, 81) = 81$
2. Now, find the GCD of 81 and 108: $\text{GCD}(81, 108) = 27$

Thus, the greatest common divisor of 324, 81, and 108 is 27.

Conclusion:

The maximum number of families that can receive equal shares of wheat, oil, and dal is 27 families.

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

1. How would the result change if the collected amount of wheat was 350 kg instead of 324 kg?
2. What is the prime factorization of each of the numbers (324, 81, 108)?
3. How can you generalize this process for any three given quantities?
4. If there were 100 families, how much wheat, oil, and dal would each family receive?
5. How is the GCD helpful in distributing resources fairly in real-life situations?

Tip: When solving problems involving equal distribution, finding the GCD of the quantities ensures that each share is a whole number and nothing is left over.