Compute the characteristic of the ring Z18 × Z15

Number of element in ${\displaystyle Z18\times Z15}$ is ${\displaystyle 18\times 15=270.}$
So, 270x will be the zero element of ${\displaystyle Z18\times Z15=\left(\begin{array}{cc}0& 0\end{array}\right)Z=\left(\begin{array}{cc}0& 0\end{array}\right)}$ of for all ${\displaystyle x\in Z18\times Z15.}$ Let nn is charactiristic of $Z18\times Z15$ then nn must divide 270 and again let ${\displaystyle (1,1)\in Z18\times Z15(1,1)\in Z}$ then ${\displaystyle n(1,1)=(n,n)\equiv (0,0)\in Z18\times Z15Z}$, that is nn must be divisible by 18 and 15, infact nn must be least common multiple of 15 and 18. So, charactiristic of ${\displaystyle Z18\times Z15=l.c.m(18,15)=90.}$