I'd recommend keeping the involved frequencies and power as low as possible. The VCO/PLL route is probably the most straightforward, but using arithmetic operations instead can be simpler at this frequency, because the filtering can be readily done with common crystals.

If you divide the 10 MHz by 5, then mix the resulting 2 MHz back with the 10, you'll get mostly 12 and 8 MHz. Double that result to get mostly 24 and 16 MHz, then filter the 16 MHz out with as fancy a filter as necessary. 16 MHz is a very common crystal frequency, so you could do that for filtering, or even make a ladder filter with a bunch of them.

With the VCO/PLL approach, the desired 16 MHz will be the highest frequency, while the arithmetic one uses 24 MHz maximum working frequency, neglecting harmonics. The logic can all be done with 74HC, at reasonable quietness and power.

Ed

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