Back in the days of "family logic," there were a few devices to which one referred as "rate multipliers," which took a high frequency clock and divided it appropriately, based on its configuration, to produce a lower frequency at ratios not commonly available with programmable counters.

You could, since your desired output frequency is extremely low, accomplish this in firmware, provided you're willing to make the required compromises in frequency precision.

As Kai has already pointed out, a PLL gives you a much better opportunity to produce what you want, and, with the aid of your MCU, you can ensure that your stability and precision are as good as they can be.

I'm not sure what you mean by "boring". There are several very low-cost CMOS frequency synthesizer IC's that would do precisely what you want with only one IC. Even the old-reliable CMOS CD4046 could, with the aid of a counter, produce a frequency output in the range you want, to excellent precision.

I'd suggest you start with Google search on "frequency multiplier". That's what I did, as I couldn't remember the device number. Keep in mind, too, that if the output symmetry doesn't meet your requirements, you can double the frequency and then divide it by two in firmware to create a perfect square wave.

RE