Let M_{n} denote the least common multiple of the integers
1, 2, 3, ..., n. For example, M_{1} = 1,
M_{2} = 2, M_{3} = 6, M_{4} =
12, M_{5} = 60, M_{6} = 60, ...

Give a complete characterization of those n for which
M_{n} = M_{n-1}.

Source: Australian Mathematical Olympiad

Can you find arbitrarily long stretches such that
M_{n} = M_{n+1}
= M_{n+2} = ... ?