  We present the first measurement of the lifetimes of Giant Molecular Clouds
(GMCs) in cosmological simulations at $z = 0$, using the Latte suite of FIRE-2
simulations of Milky Way-mass galaxies. We track GMCs with total gas mass
$\gtrsim 10^5$ M$_\odot$ at high spatial ($\sim1$ pc), mass ($7100$
M$_{\odot}$), and temporal (1 Myr) resolution. Our simulated GMCs are
consistent with the distribution of masses for massive GMCs in the Milky Way
and nearby galaxies. We find GMC lifetimes of $5-7$ Myr, or 1-2 freefall times,
on average, with less than 2$\%$ of clouds living longer than 20 Myr. We find
decreasing GMC lifetimes with increasing virial parameter, and weakly
increasing GMC lifetimes with galactocentric radius, implying that environment
affects the evolutionary cycle of GMCs. However, our GMC lifetimes show no
systematic dependence on GMC mass or amount of star formation. These results
are broadly consistent with inferences from the literature and provide an
initial investigation into ultimately understanding the physical processes that
govern GMC lifetimes in a cosmological setting.
