Problem #7

Let M_n denote the least common multiple of the integers 1, 2, 3, ..., n. For example, M₁ = 1, M₂ = 2, M₃ = 6, M₄ = 12, M₅ = 60, M₆ = 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 = ... ?

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