  A composite positive integer $n$ has the Lehmer property if $\phi(n)$ divides
$n-1,$ where $\phi$ is an Euler totient function. In this note we shall prove
that if $n$ has the Lehmer property, then $n\leq 2^{2^{K}}-2^{2^{K-1}}$, where
$K$ is the number of prime divisors of $n$. We apply this bound to repunit
numbers and prove that there are at most finitely many numbers with the Lehmer
property in the set $$ \left\{\frac{g^{n}-1}{g-1}\ \bigg|\ n,g\in\mathbb{N},\
\nu_{2}(g)+\nu_{2}(g+1)\leq L\ \right\}, $$ where $\nu_{2}(g)$ denotes the
highest power of $2$ that divides $g$, and $L\geq 1$ is a fixed real number.
