# Birthday Special #3 Aditya Raut

**Number Theory**Level 5

For positive integers \(a\), \(b\), and \(c\), define \[ f(a,b,c)=\frac{abc}{\text{gcd}(a,b,c)\cdot\text{lcm}(a,b,c)}. \] We say that a positive integer \(n\) is \(f(\lambda)\) if there exist \(x,y,z\leq60\)that satisfy \(f(x,y,z)=n\). How many \(f(\lambda)\) integers are there?