# proof lattice

• Jan 12th 2012, 05:36 AM
JK64
proof lattice
how do i prove this lattice (N0,Lowest Common Multiple (LCM) ,great common divisor (GCD)) is distributive?

• Jan 12th 2012, 06:20 AM
Plato
Re: proof lattice
Quote:

Originally Posted by JK64
how do i prove this lattice (N0,Lowest Common Multiple (LCM) ,great common divisor (GCD)) is distributive?

What does that mean?
• Jan 12th 2012, 06:29 AM
JK64
Re: proof lattice
be L a lattice

L=(N0,LCM,GCD)

in which N0= is da naturals set with zero included
LCM is the Lowest Common Multiple
GCD is the great common divisor

And i want need to prove that lattice L is dristibutive which is

a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c).

In this case i need to prove,

GCD(a,LCM(b,c)) == LCM(GCD(a,b),GCD(a,c))
• Jan 12th 2012, 06:31 AM
JK64
Re: proof lattice

i) a|/b & a|/c [which is easy to prove]
ii) a|b & a|/c
iii) a|/b & a|c
iv) a|b & a|c

ii) & iii) i think i'm close to the answer, but i'm really struggling with iv)
• Jan 12th 2012, 06:38 AM
JK64
Re: proof lattice