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One complex method
Using the 2KHz square wave signal as the reference signal of PLL, you can get a 54KHz signal, and then divided this frequency by 20, you will get 2.7Khz.
By the way, what's your application?
Use a small microcontroller - 8-pin PIC, PIAXE, or similar ..
Program one pin as input to sense transitions (high-to-low and low-to-high) of the incomming 2kHz signal and program another pin - output - to send out 2.7kHz (or whatever you need) signal as soon as it senses 2kHz on the input pin ..