why they use crystal frequency three times the required CPU clock?

Question

In the data sheets for 8284a, the said The crystal frequency should be selected at three times the required CPU clock.
why they use crystal frequency three times the required CPU clock?

Answer 1

The 8284a has a divide by 3 counter, to generate a clock with 33% duty cycle which is required to run the 8086.

source

Answer 2

To supplement C_Elegans' answer:

The 8086 requires a 33% duty cycle clock, instead of a 50% duty cycle clock, in order to optimize the internal combinatorial logic timing and to also synchronize with peripherals attached externally to the 8086.

The 8284A clock generator was included as an additional IC to make it easier on designers, by providing the required 33% duty cycle clock and some reset and bus logic functions. To keep things easier for the 8284A, the designers simply applied a divide-by-3 function in order to generate the 33% duty cycle. There are other ways of achieving this in more modern parts today, perhaps. And perhaps, if something like this were needed today, it might be handled in a less externally visible fashion. But at the time, this was the most obvious and easy path to get there.