SOLUTION: How do i show for intergers a,b and c from which at most one is 0(zero): gcd(a,gcd(b,c)) = gcd(gcd(a,b),c)

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Question 25704: How do i show for intergers a,b and c from which at most one is 0(zero):
gcd(a,gcd(b,c)) = gcd(gcd(a,b),c)
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
TO SHOW THAT
gcd(a,gcd(b,c)) = gcd(gcd(a,b),c)WHEN A OR B OR C IS ZERO.
WE KNOW THAT GCD(0,A)=A
CASE I ...LET A=0..THEN
LHS=gcd(a,gcd(b,c))=GCD(GCD(B,C))=GCD(B,C)
RHS = gcd(gcd(a,b),c)=GCD(B,C)=LHS ...PROVED
CASE II.....LET B=0...THEN
LHS=gcd(a,gcd(b,c))=GCD(A,C)
RHS = gcd(gcd(a,b),c)=GCD(A,C)=LHS....PROVED
CASE III...LET C=0....THEN
LHS=gcd(a,gcd(b,c))=GCD(A,B)
RHS = gcd(gcd(a,b),c)=GCD(GCD(A,B)=GCD(A,B)=LHS...PROVED