Two pipes are dripping in a hand wash area as there is mild leakage in the tap. Tap 1 drips every 3 minutes and tap 2 drips every 5 minutes. If at a given time they both dripped together, after how many minutes they will drip again together?

Options

A. 3
B. 15
C. 30
D. 5

Answer

To solve the problem of when both taps will drip together again, we need to find the least common multiple (LCM) of the two time intervals at which they drip.

**Step 1: Identify the time intervals**
- Tap 1 drips every 3 minutes.
- Tap 2 drips every 5 minutes.

**Step 2: Find the LCM of 3 and 5**
To find the LCM, we can use the prime factorization method or the listing multiples method. Here, we will use the prime factorization method.

- The prime factorization of 3 is \(3^1\).
- The prime factorization of 5 is \(5^1\).

**Step 3: Calculate the LCM**
The LCM is found by taking the highest power of each prime number that appears in the factorizations:

- For the prime number 3, the highest power is \(3^1\).
- For the prime number 5, the highest power is \(5^1\).

Now, multiply these together:
\[ \text{LCM} = 3^1 \times 5^1 = 3 \times 5 = 15 \]

**Step 4: Conclusion**
Thus, both taps will drip together again after 15 minutes.

### Final Answer:
Both taps will drip together again after **15 minutes**.

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