Bourque and Ligh (1992) conjectured that the least common multiple matrix on a GCD-closed set
is nonsingular. This conjecture was shown to be false by Haukkanen *et al. *(1997)
and subsequently by Hong (1999).

# Bourque-Ligh Conjecture

## See also

GCD-Closed Set, Least Common Multiple Matrix## Explore with Wolfram|Alpha

## References

Bourque, K. and Ligh, S. "On GCD and LCM Matrices."*Linear Algebra Appl.*

**174**, 65-74, 1992.Haukkanen, P.; Wang, J.; and Sillanpää, J. "On Smith's Determinant."

*Linear Alg. Appl.*

**258**, 251-269, 1997.Hong, S. "On the Bourque-Ligh Conjecture of Least Common Multiple Matrices."

*J. Algebra*

**218**, 216-228, 1999.

## Referenced on Wolfram|Alpha

Bourque-Ligh Conjecture## Cite this as:

Weisstein, Eric W. "Bourque-Ligh Conjecture."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Bourque-LighConjecture.html