WM07 said:Can you tell me if my answer is correct?
in (1 2 3 4) (1 2 3 4) The order of permutation is LCM = (4, 4) = 8
rs1n said:The order of the permutation is indeed the LCM of the order of each. However, you may want to double check your math. LCM(4,4) is not 8.
:-)
Yes, write in DISJOINT cycles and the order is then the least common
multiple of the lengths of the cycle.
LCM stands for "least common multiple" and is used to determine the smallest number that is a multiple of two or more given numbers. In the context of confirming the order of permutation, LCM is used to find the lowest number that all elements in a permutation need to be raised to in order to obtain the identity permutation.
To calculate the LCM of a set of numbers, you can use the prime factorization method. First, factor each number into its prime factors. Then, identify the highest power of each prime factor among all the numbers. Finally, multiply all the highest powers together to get the LCM.
In a permutation, the order of elements is important. To confirm the order of permutation, we need to determine the smallest number that can be used to raise each element to in order to obtain the identity permutation. LCM provides this number, as it is the smallest multiple of all the elements in the permutation.
Yes, LCM can be used for any type of permutation, as long as the elements in the permutation are integers. LCM can also be used for non-integer elements, but the calculation may become more complex.
LCM helps in confirming the order of permutation by providing the lowest number that all elements in the permutation need to be raised to in order to obtain the identity permutation. This allows us to determine the order of the permutation and confirm its correctness.