Solution: To find when both projects synchronize, compute the least common multiple (LCM) of 10 and 15. Factorize: $10 = 2 \times 5$ and $15 = 3 \times 5$. The LCM is $2 \times 3 \times 5 = 30$. Thus, the projects will align after $\boxed30$ months. - Nelissen Grade advocaten