We present $emph{NuSTAR}$ observations of neutron star (NS) low-mass X-ray binaries: 4U 1636-53, GX 17+2, and 4U 1705-44. We observed 4U 1636-53 in the hard state, with an Eddington fraction, $F_{mathrm{Edd}}$, of 0.01; GX 17+2 and 4U 1705-44 were in the soft state with fractions of 0.57 and 0.10, respectively. Each spectrum shows evidence for a relativistically broadened Fe K$_{alpha}$ line. Through accretion disk reflection modeling, we constrain the radius of the inner disk in 4U 1636-53 to be $R_{in}=1.03pm0.03$ ISCO (innermost stable circular orbit) assuming a dimensionless spin parameter $a_{*}=cJ/GM^{2}=0.0$, and $R_{in}=1.08pm0.06$ ISCO for $a_{*}=0.3$ (errors quoted at 1 $sigma$). This value proves to be model independent. For $a_{*}=0.3$ and $M=1.4 M_{odot}$, for example, $1.08pm0.06$ ISCO translates to a physical radius of $R=10.8pm0.6$ km, and the neutron star would have to be smaller than this radius (other outcomes are possible for allowed spin parameters and masses). For GX 17+2, $R_{in}=1.00-1.04$ ISCO for $a_{*}=0.0$ and $R_{in}=1.03-1.30$ ISCO for $a_{*}=0.3$. For $a_{*}=0.3$ and $M=1.4 M_{odot}$, $R_{in}=1.03-1.30$ ISCO translates to $R=10.3-13.0$ km. The inner accretion disk in 4U 1705-44 may be truncated just above the stellar surface, perhaps by a boundary layer or magnetosphere; reflection models give a radius of 1.46-1.64 ISCO for $a_{*}=0.0$ and 1.69-1.93 ISCO for $a_{*}=0.3$. We discuss the implications that our results may have on the equation of state of ultradense, cold matter and our understanding of the innermost accretion flow onto neutron stars with low surface magnetic fields, and systematic errors related to the reflection models and spacetime metric around less idealized neutron stars.
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