How many PCR cycles before you must worry about contamination?

I'm trying to find out about how many PCR cycles DNA/RNA must go through before there's a significant worry about the resulting amplicon contaminating other reactions. For example, if I only amplify a plate of genomics through 15 cycles, do I need to take the precaution of keeping it completely contained in a post-amplification room or would there be a small enough risk to not worry about taking it in a sealed plate out into the neutral laboratory space for reading of the results?