Some help with these would be appreciated

1. Prove that if gcd(a,b)=1 and gcd(a,c)=1 then gcd(a,bc)=1

2. Prove that if a and b are relatively prime and c|a, then c and b are relatively prime

3. Prove that if a is odd, then 24|a(a^2-1)

4. Prove that if a and b are relatively prime, then gcd(a+b,a-b)=1 or 2

5. Prove that, if a and b are relatively prime, then so are a^n and B^n, where a and b and n are positive integers

6. Prove that lcm(a,b)xgcd(a,b)=ab