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There are 60 minutes in one hour. Therefore, 1140 minutes is equal to 1140/60 = 19 hours.
LCM(6, 20, 19) = 1140
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If it had n sides, the sum of its interior angles would have been (n-2)*180 degrees. That would require (n-2)*180 = 1140 This requires that 180 divides into 1140. It does not so there is no such polygon.
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