For positive integers aaa, bbb, ccc, which of the following is NOT always true?
gcd(gcd(a,b),c)=gcd(a,gcd(b,c))\gcd(\gcd(a, b), c) = \gcd(a, \gcd(b, c))gcd(gcd(a,b),c)=gcd(a,gcd(b,c)) (associativity)
lcm(gcd(a,b),gcd(a,c))=gcd(a,lcm(b,c))\text{lcm}(\gcd(a, b), \gcd(a, c)) = \gcd(a, \text{lcm}(b, c))lcm(gcd(a,b),gcd(a,c))=gcd(a,lcm(b,c))
gcd(a,b)⋅lcm(a,b)=a⋅b\gcd(a, b) \cdot \text{lcm}(a, b) = a \cdot bgcd(a,b)⋅lcm(a,b)=a⋅b
lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))\text{lcm}(a, \gcd(b, c)) = \gcd(\text{lcm}(a, b), \text{lcm}(a, c))lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))