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Everything we've seen in the last 6 years has a height of 151/2" to 171/2".
The general rule used is that the TOP of the microwave (where it touchs the cabinets) should be no less than 66" from the floor (or 30" from the top of the range).
We will not install a microwave if it is less than those dimensions.
Older cabinets were sometimes lower and in those cases you shouldn't install an over-the-range microwave oven.
You can have more height you just can't have less.
Please let me know if you would like more information and/or clarification.