The term DPI (dots per inch) is often used interchangeably with PPI, which is confusing. A DPI camera setting doesn't make any sense, it doesn't recognise dots. DPI is only relevant at the printing stage. You change it with your image editing software. Changing the image's DPI setting on your computer doesn't change your image, it adds to it some instructions for your printer. 240-300ppi is considered suitable for prints, but print quality is primarily limited by the number of pixels in your image, not by the DPI, as explained below.
An image with few pixels set at 300dpi might produce a high quality image, but it would be very small. If you reduce the DPI to 72dpi the same print would be bigger, but of inferior quality. By selecting the lower DPI you are essentially stretching the file and reducing the density of dots per inch of your image. Fewer dots and your image degrades, which is called pixilation. 72dpi is generally suitable for images which will be viewed only on a monitor, or for use on the Web. When a printer asks you for images at 300dpi they actually want a image with enough pixels for the required print size with 300 dots per inch in each square inch.
When you need to change your image's DPI in Photoshop, copy your file with a new name, then select Image/Image size, or Image Resize, make sure the Resample Image box is unticked, insert your preferred DPI setting in the Resolution box, and click OK. Please note Photoshop is using the term PPI here, instead of DPI. When changing your DPI your editing software may re-sample your image as a default, and your image will lose data. If you don't resample the image, no data is lost, and your printing company can adjust the DPI as they see fit. This technique is explained in the following YouTube video.
This article is a basic introduction to this topic. For a more technical explanation try the following link: