  The escape of ultraviolet photons from the densest regions of the
interstellar medium (ISM) --- Giant Molecular Clouds (GMCs) --- is a poorly
constrained parameter which is vital to understanding the ionization of the ISM
and the intergalactic medium. We characterize the escape fraction,
f$_{\text{esc,GMC}}$, from a suite of individual GMC simulations with masses in
the range 10$^{4-6}$ M$_{\odot}$ using the adaptive-mesh refinement code FLASH.
We find significantly different f$_{\text{esc,GMC}}$ depending on the GMC mass
which can reach $>$90% in the evolution of 5$\times$10$^4$ and 10$^{5}$
M$_{\odot}$ clouds or remain low at $\sim$5% for most of the lifetime of more
massive GMCs. All clouds show fluctuations over short, sub-Myr timescales
produced by flickering HII regions. We combine our results to calculate the
total escape fraction (f$_{\text{esc,tot}}$) from GMC populations in dwarf
starburst and spiral galaxies by randomly drawing clouds from a GMC mass
distribution (dN/dM$\propto$M$^{\alpha}$, where $\alpha$ is either -1.5 or
-2.5) over fixed time intervals. We find typical f$_{\text{esc,tot}}$ values of
8% for both the dwarf and spiral models. The fluctuations of
f$_{\text{esc,tot}}$, however, are much larger for the dwarf models with values
as high as 90%. The photons escaping from the 5$\times$10$^4$ and 10$^{5}$
M$_{\odot}$ GMCs are the dominant contributors to f$_{\text{esc,tot}}$ in all
cases. We also show that the accompanying star formation rates (SFRs) of our
model ($\sim$2$\times$10$^{-2}$ and 0.73 M$_{\odot}$yr$^{-1}$) are consistent
with observations of SFRs in dwarf starburst and spiral galaxies, respectively.
