Aakriti decided to distribute milk in an orphanage on her birthday. The supplier brought two milk containers which contain 398 l and 436 l of milk. The milk is to be tranferred to another containers so that 7 l and 11 l of milk is left in both the containers respectively. What will be the maximum capacity of the drum?

Answer

To solve the problem step by step, we need to determine the maximum capacity of the drum that can be used to transfer milk from the two containers while leaving the specified amounts of milk in each container.

### Step-by-Step Solution:

1. **Identify the initial amounts of milk in the containers:**
- Container 1: 398 liters
- Container 2: 436 liters

2. **Determine the amount of milk that will be left in each container after transferring the milk:**
- Milk left in Container 1: 7 liters
- Milk left in Container 2: 11 liters

3. **Calculate the amount of milk that will be transferred from each container:**
- For Container 1:
\[ \text{Milk transferred} = 398 - 7 = 391 \text{ liters} \]
- For Container 2:
\[ \text{Milk transferred} = 436 - 11 = 425 \text{ liters} \]

4. **Find the maximum capacity of the drum, which is the highest common factor (HCF) of the amounts transferred (391 liters and 425 liters).**

5. **Use the Euclidean algorithm to find the HCF of 391 and 425:**
- Divide 425 by 391:
\[ 425 = 391 \times 1 + 34 \]
- Now, take 391 and divide it by the remainder 34:
\[ 391 = 34 \times 11 + 17 \]
- Next, take 34 and divide it by the remainder 17:
\[ 34 = 17 \times 2 + 0 \]
- Since the remainder is now 0, the last non-zero remainder is the HCF.

6. **Conclusion:**
- The HCF of 391 and 425 is 17.
- Therefore, the maximum capacity of the drum is **17 liters**.

### Summary:
The maximum capacity of the drum that Aakriti can use to transfer milk while leaving the specified amounts in the containers is **17 liters**.