John Campbell's lcm refinement algorithm

Here a0,...,an-1 are integers, with a0,...,an-1 positive.

We replace them by an array of positive integers b0,...,bn-1, where

  1. bi divides ai for 0 ≤ i < n;
  2. gcd(bi, bj)=1 for 0 ≤ i < j < n;
  3. lcm(a0,...,an-1)=lcm(b0,...,bn-1)=b0···bn-1.
The algorithm is due to T.J. Stieltjes, Oeuvres Complètes, Tome II, 280-283 (from Sur la theorie des nombres, Ann. Fac. Toulouse 4 (1890), 1-103, especially Sections 18-19) and was rediscovered by John Campbell in 2003. See note.

Enter the positive integers (separated by spaces):

Last modified 11th August 2006
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