#Pip, 41 bytes

Not a competing answer, since language is newer than question. But that GolfScript mark of 68 needed to come down.

Fi2,++a{p:0T$|g%i{++pg/:i}Ipx.:i.'^.p.s}x

Output ends in a space; if that's a problem, the following version is also 41 bytes (including the -s flag):

Fi2,++a{p:0T$|g%i{++pg/:i}IplAE:i.'^.p}l

Formatted, with explanations:

F i 2,++a {      For i in range(2,a+1); note ++ used to avoid parentheses in 2,(a+1)
  p:0            p will store the greatest power of i that divides both numbers
  T $+(g%i) {    Loop till the sum of g%i is nonzero, where g is a list initialized
                  from cmdline args
    ++p          As long as g%i is [0 0], increment p...
    g/:i         ...and divide both numbers in g by i
  }
  I p            If p is nonzero, i went into both numbers at least once
    x.:i.'^.p.s  Append i^p and a space to the result
}
x                Print the result

Pip, unlike GolfScript, CJam, et al. is an imperative language with infix operators; it also takes some inspiration from array-programming languages. This task nicely displays both paradigms at work.

(Note that the 2015-4-20 commit is needed to run this, since I just fixed a couple of bugs.)

Pip, 41 bytes

Not a competing answer, since language is newer than question. But that GolfScript mark of 68 needed to come down.

Fi2,++a{p:0T$|g%i{++pg/:i}Ipx.:i.'^.p.s}x

Output ends in a space; if that's a problem, the following version is also 41 bytes (including the -s flag):

Fi2,++a{p:0T$|g%i{++pg/:i}IplAE:i.'^.p}l

Formatted, with explanations:

F i 2,++a {      For i in range(2,a+1); note ++ used to avoid parentheses in 2,(a+1)
  p:0            p will store the greatest power of i that divides both numbers
  T $+(g%i) {    Loop till the sum of g%i is nonzero, where g is a list initialized
                  from cmdline args
    ++p          As long as g%i is [0 0], increment p...
    g/:i         ...and divide both numbers in g by i
  }
  I p            If p is nonzero, i went into both numbers at least once
    x.:i.'^.p.s  Append i^p and a space to the result
}
x                Print the result

Pip, unlike GolfScript, CJam, et al. is an imperative language with infix operators; it also takes some inspiration from array-programming languages. This task nicely displays both paradigms at work.

(Note that the 2015-4-20 commit is needed to run this, since I just fixed a couple of bugs.)