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The linear canonical transform (LCT) is a generalization of the fractional Fourier transform (FRFT) having applications in several areas of signal processing and optics. In this paper, we extend the uncertainty principle for real signals in the fractional Fourier domains to the linear canonical transform domains, giving us the tighter lower bound on the product of the spreads of the signal in two specific LCT domains than the existing lower bounds in the LCT domains. It is seen that this lower bound can be achieved by a Gaussian signal. The effect of time-shifting and scaling the signal on the uncertainty principle is also discussed. It is shown here that a signal bandlimited in one LCT domain can be bandlimited in some other LCT domains also. The exceptions to the uncertainty principle in the LCT domains arising out of this are also discussed.