document.write( "Question 25704: How do i show for intergers a,b and c from which at most one is 0(zero):
\n" ); document.write( "gcd(a,gcd(b,c)) = gcd(gcd(a,b),c) \n" ); document.write( "

Algebra.Com's Answer #13842 by venugopalramana(3286) $\"\"$ $\"About$

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TO SHOW THAT
\n" ); document.write( "gcd(a,gcd(b,c)) = gcd(gcd(a,b),c)WHEN A OR B OR C IS ZERO.
\n" ); document.write( "WE KNOW THAT GCD(0,A)=A
\n" ); document.write( "CASE I ...LET A=0..THEN
\n" ); document.write( "LHS=gcd(a,gcd(b,c))=GCD(GCD(B,C))=GCD(B,C)
\n" ); document.write( "RHS = gcd(gcd(a,b),c)=GCD(B,C)=LHS ...PROVED
\n" ); document.write( "CASE II.....LET B=0...THEN
\n" ); document.write( "LHS=gcd(a,gcd(b,c))=GCD(A,C)
\n" ); document.write( "RHS = gcd(gcd(a,b),c)=GCD(A,C)=LHS....PROVED
\n" ); document.write( "CASE III...LET C=0....THEN
\n" ); document.write( "LHS=gcd(a,gcd(b,c))=GCD(A,B)
\n" ); document.write( "RHS = gcd(gcd(a,b),c)=GCD(GCD(A,B)=GCD(A,B)=LHS...PROVED \n" ); document.write( "

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