Glossary
DPI
Short answer
Dots per inch in print; the measure of print quality.
DPI only means something in print; there is no DPI on screen, only pixels. An image being "72 DPI" is a label in the file and does not change its pixel count.
The print standard is 300 DPI. To find the pixels you need, multiply the print size in inches by 300.
Because AI output does not come out at that size, an upscaling step is almost always necessary for print work.
Example
A3 is roughly 11.7 × 16.5 inches. At 300 DPI that needs 3510 × 4950 pixels.