$(1+1/x)(1+1/y)(1+1/z) = 3$ Find all possible integer values of $x$, $y$, $z$ given all of them are positive integers. Find all possible integer values of $x$, $y$, $z$ given all of them are positive integers
and 
$$(1+1/x)(1+1/y)(1+1/z) = 3.$$
I know
$(x+1)(y+1)(z+1) = 3xyz$ which is no big deal. I can't move forward now.
morever it is given $x$ is less than or equal to $y$ and $y$ is less than or equal to $z$

Hint: Suppose that $x, y, z \ge 3$. Then $$1 + \frac 1 x \le \frac{4}{3}$$
and likewise for the other two. Then
$$\left(1 + \frac 1 x\right)\left(1 + \frac 1 y\right)\left(1 + \frac 1 z\right) \le \frac{64}{27} < 3$$
So one of the numbers has to be pretty small; now consider cases with $x = 1$ and $x = 2$.

Something else that you know: $3$ is a divisor of the right side, so it's a divisor of the left side. Since $3$ is prime, $3$ has to divide one of the individual terms.
