### John Campbell's lcm refinement algorithm

Here a_{0},...,a_{n-1} are integers, with a_{0},...,a_{n-1} positive.
We replace them by an array of positive integers b_{0},...,b_{n-1}, where

- b
_{i} divides a_{i} for 0 ≤ i < n;
- gcd(b
_{i}, b_{j})=1 for 0 ≤ i < j < n;
- lcm(a
_{0},...,a_{n-1})=lcm(b_{0},...,b_{n-1})=b_{0}···b_{n-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.

*Last modified 11th August 2006*

Return to main page