Comment by throwaway81523

I just did a dumb search with lazy lists in Haskell, inspired by the famous problem about Hamming numbers. Runtime was 0.02 seconds. About 2 more seconds to fine the one after that (results: [1,40755,1533776805,57722156241751]).

    import           Data.Ord

    tri n = n*(n+1)`quot`2
    pent n = n*(3*n-1)`quot`2
    hex n = n*(2*n-1)

    fs :: (Integer -> Integer)->[Integer]
    fs f = map f [1..]

    cm aas@(a:as) bbs@(b:bs)
       = case compare a b of
           EQ -> a : cm as bs
           GT -> cm aas bs
           LT -> cm as bbs

    tt = (fs tri) `cm` (fs pent) `cm` (fs hex)

    main = print . take 3 $ tt

Added: the one after that is 2172315626468283465 which took about 6 minutes with the same Haskell program. I'm sure there are faster implementations and better algorithms. I didn't try to search any further.