### periodicity of a word

I have the following code to create words.

sage: M.<x,y,z> = FreeMonoid(3)
sage: Word(x^3*y*x*z^2*x)
word: xxxyxzzx

I want find the periodicity of a given word.

For example ababab has periodicity 3 and abcdabcde has periodicity 1.

~~Kindy ~~Kindly help me with this.

Thank you.