Calculate the order in cycle notation 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
 A: 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 $(132)$.
A: Since you have the products of disjoint cycles, what do you know about the order of a cycle?
For a single cycle, its order is equal to its length. 
The order of a product of disjoint cycles, as yours are, is equal to the least common multiple $(\operatorname{lcm})$ of the the orders of the cycles that form it, i.e., the least common multiple of the lengths of the disjoint cycles.
E.g. the order of $(1 2 3 4 5 6 7)$ is $7$. The order of $(123)(4567) = \operatorname{lcm}\,(3, 4) = 12$.
The order of $(123)(456)(7) = \operatorname{lcm}\,(3, 3, 1) = 3$.
Now, can you apply that to your permutations to find their orders?
A: Hint: Find the least common multiple of the orders of each disjoint cycle.
