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How bad is it to leak $k$ in RSA?

In RSA using a small public exponent $e$ such as $65537$, how bad is it if the value $k$ leaks? $k$ as in the following equations:

$ed – 1 = k phi(n)$

or

$ed – 1 = k cdot mathrm{lcm}(p-1,q-1)$

Intuitively, this would only reduce the complexity of the breaking the system by $65535$ times, nowhere near enough to matter, though I assume that GNFS would not be improved by knowing $k$.

How bad is it to leak $k$ in RSA?

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