Suppose G is some cyclic group order n. If we know for some a ∈ G that a5 = e and a11 = e, then what is the smallest order G may take?

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Suppose G is some cyclic group order n. If we know for some a ∈ G that a<sup>5</sup> = e and a<sup>11</sup> = e, then what is the smallest order G may take?