Giving a range to Plot to plot multiple lines at the same time

I’d like to plot something like this:

Except that instead of manually specifying all the functions to be plotted, I specify a range. So for example I could feed the command Range[0,6,2] to get it to plot four lines on the same plot, i.e. $mathrm{Sin}[0],mathrm{Sin}[2x],mathrm{Sin}[4x]$ and $mathrm{Sin}[6x]$.

How can I do this? I tried Plot[Sin[# x], {x, 0, 2 Pi}] & /@ Range[1, 3] which yields the desired three lines, but each in their own plot as opposed to one. Attempting to map twice with Plot[#, {x, 0, 2 Pi}] & /@ {Sin[# x] /@ Range[1, 3]} yields no plot at all.

Attributes[Sin]

(* {Listable, NumericFunction, Protected} *)

Plot[Evaluate@Sin[Range[3] x], {x, 0, 2 Pi},
 PlotLegends -> "Expressions"]

Plot[Sin[# x] & /@ Range[1, 3] // Evaluate, {x, 0, 2 Pi}]

Show[Plot[Sin[# x], {x, 0, 2 Pi}] & /@ Range[1, 3] ]

Plot[Table[Sin[om x], {om, Range[1, 3] }] // Evaluate, {x, 0, 2 Pi}]