To find the least perfect square number that is divisible by 3, 4, 5, 6, and 8, follow these steps:

1. Find the Least Common Multiple (LCM):
- First, determine the prime factorization of each number:
- \( 3 = 3 \)
- \( 4 = 2^2 \)
- \( 5 = 5 \)
- \( 6 = 2 \times 3 \)
- \( 8 = 2^3 \)

- Combine the highest powers of all prime factors:
- The highest power of 2 is \( 2^3 \) (from 8)
- The highest power of 3 is \( 3 \) (from 3 or 6)
- The highest power of 5 is \( 5 \) (from 5)

- The LCM of 3, 4, 5, 6, and 8 is:
\[
\text{LCM} = 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120
\]

2. Make the LCM a Perfect Square:
- The prime factorization of 120 is \( 2^3 \times 3 \times 5 \).
- To be a perfect square, each prime factor must appear to an even power:
- \( 2^3 \) needs one more 2 to make it \( 2^4 \).
- \( 3 \) needs one more 3 to make it \( 3^2 \).
- \( 5 \) needs one more 5 to make it \( 5^2 \).

- Therefore, the smallest perfect square that includes these factors is:
\[
2^4 \times 3^2 \times 5^2 = 16 \times 9 \times 25
\]

- Calculate:
\[
16 \times 9 = 144
\]
\[
144 \times 25 = 3600
\]


The least perfect square number which is divisible by 3, 4, 5, 6, and 8 is 3600.

The correct answer is D. 3600.