I don't quite understand the meaning of "a watch losing 0.15 s every minute" but I'm going to assume that s means seconds.

By using dimensional analysis:
 \frac{0.15 seconds}{} * \frac{1 minute}{60 seconds} = 2.5*10^{-3} minutes

Using dimensional analysis again for a day, we get:
 \frac{1 day}{}* \frac{24 hours}{1 day} * \frac{60 minutes}{1 hour} =1440 minutes

Dividing the two, (2.5*10^{-3})/1440 = 1.736*10^{-6} minutes

Sorry, but I'm kind of doubting my answer. Please check other sources or wait for another person to answer and confirm this. Thank you!