Complete Lattice: Greatest Common Divisor

Complete Lattice: Greatest Common Divisor
It is sometimes useful to define gcd(0, 0) = 0 and lcm(0, 0) = 0 because then the natural numbers become a complete distributive lattice with gcd as meet and lcm as join operation.[18] This extension of the definition is also compatible with the generalization for commutative rings given below.

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