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?