What is the maximum order of any element in $A_{10}$?
My attempt: I tried this problem. But I am not sure about the answer. My answer is 21 because 10 can be written as 7+3. $A_{10}$ can have two disjoint cycle of length 7 and 3. Lcm of 7 and 3 is 21 which is the maximum order of an element of $A_{10}$. Is it correct? If not please guide me.