Digital file volume, whether it is expressed in KB, MB or GB, is not relevant for determining whether an image is suitable for printing at a particular size. What is important is the number of pixels along the sides that are available for each inch of print. Generally, the commercial machines are designed to work best when fed 300 pixels per inch and the caring/fussy photographer will submit his work with those dimensions. E.g., for an 8x10 ideally send 2400 x 3000 pixels. But the printer operators are fairly liberal in their demands because their intake software can resize the image to the needed 300 ppi. However, all resizing does have a price in quality and I imagine they would be reluctent to accept less than 150 ppi. Another factor that comes into play is that the larger the print, the greater the viewing distance and the harder it is to judge quality. Thus, for large wall-hanging prints they might accept 100 ppi. If because of a small native size or extensive cropping, you have too few pixels, I believe it is better to use Lightroom's Export resizing than to leave it to the lab.
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