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Question: Calculate the largest possible order of any permutation in S10.

My approach: List out all possible order in S10 then find the LCM of each, got lcm(5,3,2) = 30 as the largest possible order.

I'm just wondering if there's a quicker method to solve this question as it took me like forever to list out each possible orders and find their LCM respectively.

sasaki085
  • 55
  • You're forgetting the constraint that the cycles have to be disjoint in the decomposition of a permutation. – Bernard Nov 16 '20 at 10:04

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