when the sum of some fractions be $1$

prove if we want that the sum of some fractions be $1$ and the denominators of one of them is $d$ then another denominators should divisible by $d$ or $d$ should be divisible to another denominators.

It seems to be easy I tried to prove it.I first tried some cases.

$1=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$

Here we can see that $6$ is divisible by $3$. Also here $6$ is divisible by $2$ .But I want to prove one of the denominators but here two of them is possible.After trying a lot I cannot found any proofs.Any hints?

update1: the numerator should be prime

prove if we want that the sum of some fractions be $1$ and the denominators of one of them is $d$ then another denominators should divisible by $d$ or $d$ should be divisible to another denominators.

It seems to be easy I tried to prove it.I first tried some cases.

$1=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$

Here we can see that $6$ is divisible by $3$. Also here $6$ is divisible by $2$ .But I want to prove one of the denominators but here two of them is possible.After trying a lot I cannot found any proofs.Any hints?

update1: the numerator should be prime