Draw a times table (also called modular multiplication circle) of a number \$n\$ with \$k\$ vertices

Python 2, 280 241 235 233 bytes

from math import*
n,k=input()
a=2*pi/k
s='<svg viewBox="-49 -49 98 98"><circle r="49"/><path d="'
p=0;exec"s+='M%f,%f L%f,%f '%(49*cos(p),49*sin(p),49*cos(p*n),49*sin(p*n));p+=a;"*k
open('c.svg','w').write(s+'" stroke="red"/></svg>')

Try it online!

Saved 35 bytes due to removing xmlns attribute at the encouragement of qwr; and 4 more since %k was not required. 4 more by using exec instead of for i in range(k).

Writes an SVG file named c.svg. Look, ma! No graphics library! :)

Python 2 with pylab, 133 129 bytes

from pylab import*
n,k=input()
gca().add_patch(Circle((0,0),1))
a=2*pi/n
for i in range(n):c=i*a,k*i*a;plot(cos(c),sin(c))
show()

Saved 4 bytes thanks to Mr. Xcoder.

JavaScript (ES6), 207 206 bytes

with(Math)f=(k,n,g=i=>[cos(i*=PI*2/k),sin(i)])=>`<svg viewBox=-1,-1,2.01,2.01><circle r=1 fill=none${s=` stroke=#000 stroke-width=.01 `}/><path d=M${[...Array(k)].map((_,i)=>g(i)+`L`+g(i*n)).join`M`}${s}/>`
;o.innerHTML=f(27,2)

<div oninput=o.innerHTML=f(+k.value,+n.value)><input type=number min=2 value=27 id=k><input type=number min=2 value=2 id=n><div id=o>

Output of the function is an HTML5-compatible SVG snippet. The function itself is the first line of the snippet, the rest of the snippet merely serves to demonstrate the function. Edit: Saved 1 byte thanks to @Arnauld.