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\text{LCM}(15, 25) = 3 \cdot 5^2 = 3 \cdot 25 = 75
Therefore, both systems will align at the start after $ \boxed{75} $ seconds.
Question: A geographer is studying a triangular grid of weather stations where true equilateral triangles have sides aligned to a coordinate system based on modulo $6$ symmetry. If the distance between adjacent stations in one direction is $60$ km, how many integer-coordinate points (lattice points) lie strictly inside a large equilateral triangle with side length $6$ units (in km), assuming the vertices are at lattice points satisfying modular constraints?

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