how to prove or disprove the following :-
$$\gcd (kn,km) = k\gcd(n,m).$$
$$\operatorname{lcm}(n,m)\gcd(n,m)=mn.$$
$$\operatorname{lcm}(kn,km)=k\operatorname{lcm}(n,m).$$
how to prove or disprove the following :-
$$\gcd (kn,km) = k\gcd(n,m).$$
$$\operatorname{lcm}(n,m)\gcd(n,m)=mn.$$
$$\operatorname{lcm}(kn,km)=k\operatorname{lcm}(n,m).$$