  We study the temporal and energy spectral characteristics of the persistent
black hole X-ray binary LMC X-1 using two XMM-Newton and a Suzaku observation.
We report the discovery of low frequency (~ 26-29 mHz) quasi-periodic
oscillations (QPOs). We also report the variablity of the broad iron K-alpha
line studied earlier with Suzaku. The QPOs are found to be weak with fractional
rms amplitude in the ~ 1-2 % range and quality factor Q~2-10 . They are
accompanied by weak red noise or zero-centered Lorentzian components with rms
variability at the ~ 1-3 % level. The energy spectra consists of three varying
components - multicolour disk blackbody (kT_{in} ~ 0.7-0.9 keV), high energy
power-law tail (Gamma ~ 2.4 - 3.3) and a broad iron line at 6.4-6.9 keV. The
broad iron line, the QPO and the strong power-law component are not always
present. The QPOs and the broad iron line appear to be clearly detected in the
presence of a strong power-law component. The broad iron line is found to be
weaker when the disk is likely truncated and absent when the power-law
component almost vanished. These results suggest that the QPO and the broad
iron line together can be used to probe the dynamics of the accretion disk and
the corona.
