Is there enough slices 2?

Discrete Mathematics Level 4

A man is again hired to cut cake at a party. He was informed the day before the party that out of total of \(48\) people, \(40\) people could definitely attend the party but \(8\) persons weren't sure if they could make it or not. To make sure everything would be fair, he decided the cut the circular cake into slices such that if either \(48\) or \(40\) people attended the party, the cake could be distributed evenly to all attendees. At first he thought he needed LCM(\(40\) ,\(48\)) = \(240\) slices but his wife informed him that he was being an idiot . Such an intelligent wife !!!!!!

What is the minimum number of slices the cake cutter needs to slice the cake into such that either \(40\) or \(48\) people can attend the party and the cake can still be distributed evenly?


P.S. Can you generalise your answer for \(m\), \(n\) people?


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