Question
What are some inequalities involving the greatest common divisor (GCD) function?
Typical Answer
$$\gcd(a,bc) \leq \gcd(a,b)\gcd(a,c)$$
My Attempt
I tried checking the Wikipedia page, but the properties listed there for the greatest common divisor (GCD) function are all in the form of equations.
Can you recommend an online resource/textbook/reference that lists properties for the GCD function in the form of inequalities?