c))} lcm ( a , gcd ( b , c ) ) = gcd ( lcm ( a , b ) , lcm ( a , c ) ) {\displaystyle \operatorname {lcm} (a,\gcd(b,c))=\gcd(\operatorname {lcm} (a
gcd ( y , z ) ) = gcd ( x , y , z ) lcm ( lcm ( x , y ) , z ) = lcm ( x , lcm ( y , z ) ) = lcm ( x , y , z ) } ∀ x , y , z ∈ Z . {\displaystyle