# Birthday Special #3 Aditya Raut

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?

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