Can two positive integers have gcd(a,b)=20\gcd(a, b) = 20gcd(a,b)=20 and lcm(a,b)=300\text{lcm}(a, b) = 300lcm(a,b)=300?
No, because 20 does not divide 300
Yes, for example a=60a = 60a=60 and b=100b = 100b=100
No, because gcd\gcdgcd must equal lcm\text{lcm}lcm divided by a prime
Yes, but only if a=ba = ba=b