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<p/> <p>We are concerned with the following second-order <inline-formula> <graphic file="1687-2770-2011-867615-i2.gif"/></inline-formula>-Laplacian dynamic equations on time scales <inline-formula> <graphic file="1687-2770-2011-867615-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-867615-i4.gif"/></inline-formula>, with integral boundary conditions <inline-formula> <graphic file="1687-2770-2011-867615-i5.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-867615-i6.gif"/></inline-formula>. By using Legget-Williams fixed point theorem, some criteria for the existence of at least three positive solutions are established. An example is presented to illustrate the main result.</p>