TITLE: Calculate the order in cycle notation
QUESTION [8 upvotes]: Please help calculate the order of x and y. Let x and y denote permutations of $N(7)$ - Natural numbers mod 7  . Cycle notation: 
$$x= (15)(27436) $$
$$y= (1372)(46)(5)$$
Thanks

REPLY [2 votes]: we start from left cycle. in the left cycle we have $1\to2$ and in the right cycle we have $2\to3$, so we deduce that $1\to3$.
now in the left cycle we have $3\to1$ and in the right cycle we have $1 \to 2$, so we deduce that 3$\to2$. 
Finally in the left cycle we have$ 2\to3$ and in the right cycle we have $3 \to 1$, so we deduce that $2\to1$.
So we have in product of this two cycles $1\to3$ and $3\to2$ and $2\to1 $that is the cycle $(132)$.