Another variation on the previous puzzle

[chuckro]

CHUCKRO = CROSSBOW
1. All vowels represent prime numbers. All consonants represent non-prime numbers.
2. No letter represents zero, and no two different letters represent the same number.
3. Assuming the letters are multiplied, what is the smallest product that makes this statement true?

(If you can give a mapping with your answer, that'd be useful to me for editing purposes. But it's not strictly necessary.)

Comments

[edgehopper.livejournal.com]

I have a number of multiple mappings, but I never come out with anything smaller than 69,120.

Example:
B 12
C 1
H 8
K 360
O 2
R 4
S 6
U 3
W 10

Example 2:
B 10
C 4
H 15
K 6
O 2
R 8
S 1
U 3
W 54

Prime factorization works wonders, but I'm still don't know how to prove that there's nothing smaller than 69,120.

[chuckro.livejournal.com]

I got 46080, using a mutant variant of prime factorization. And I'm pretty sure my solution is valid. Thoughts?

B 6
C 8
H 12
K 10
O 2
R 1
S 4
U 3
W 15

[edgehopper.livejournal.com]

Ah, that is better. Not a big fan of this type of number puzzle, though.