CJam, 13 bytes
q~{\_p1$/)*}* Input as a CJam-style list. Output is linefeed separated.
[Test it here.][1]
Explanation
q~ e# Read and evaluate input. { e# Fold this block over the list (i.e. "foreach except first")... \ e# Swap with previous value. _p e# Duplicate and print previous value. 1$ e# Copy current value. / e# Integer division. )* e# Increment and multiply current value by the result. }* The final value is left on the stack and printed automatically at the end.
[1]: http://cjam.aditsu.net/#code=q~%7B%5C_p1%24%2F)%7D&input=%5B15%208%2012%2047%2022%2015%204%2066%2072%2015%203%204%5D