Minimum values of the Carmichael function

The Carmichael function λ(n) is defined as the smallest positive integer m such that a^m = 1 modulo n for all integers a coprime with n. For example λ(8) = 2 and λ(240) = 4.

Define L(n) as the smallest positive integer m such that λ(k) ≥ n for all k ≥ m. For example, L(6) = 241 and L(100) = 20 174 525 281.

Find L(20 000 000). Give the last 9 digits of your answer.

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