To determine which number is divisible by 3, 4, 5, and 6, we need to find the least common multiple (LCM) of these numbers and then check which option is divisible by this LCM.

1. Prime Factorization:
- 3: \(3\)
- 4: \(2^2\)
- 5: \(5\)
- 6: \(2 \times 3\)

2. LCM Calculation:
- Take the highest power of each prime:
- For 2: \(2^2\) (from 4)
- For 3: \(3\) (from 3 or 6)
- For 5: \(5\) (from 5)

- Calculate the LCM:
\[
\text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60
\]

3. Check Divisibility by 60:

- 30: Not divisible by 60.
- 48: Not divisible by 60.
- 75: Not divisible by 60.
- 120: Divisible by 60.


The number that is divisible by 3, 4, 5, and 6 is 120.

Thus, the correct answer is D. 120.