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.
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