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 ( \sim 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 \sim 1 - 2 \% range and quality factor Q \sim 2 - 10 . They are accompanied by weak red noise or zero-centered Lorentzian components with rms variability at the \sim 1 - 3 \% level . The energy spectra consists of three varying components – multicolour disk blackbody ( kT _ { in } \sim 0.7 - 0.9 { ~ { } keV } ) , high energy power-law tail ( \Gamma \sim 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 .