I figure we can take it for granted that said station continues to announce its broadcast frequency as 'kilocycles' instead of 'kilohertz'.
But of course it should be announced as 'kilocycles/second!
As basic physics has taught us, 1 hertz = 1 cycle/second.
Link:
https://en.wikipedia.org/wiki/HertzThe hertz (symbol: Hz) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second.[1] It is named for Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (103 Hz, kHz), megahertz (106 Hz, MHz), gigahertz (109 Hz, GHz), terahertz (1012 Hz, THz), petahertz (1015 Hz, PHz), and exahertz (1018 Hz, EHz).
Some of the unit's most common uses are in the description of sine waves and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the speeds at which computers and other electronics are driven.