# Modulo makes it weak

Consider a smallest positive integer $$P$$ which is divisible by all natural numbers from $$1$$ to $$100$$ inclusive. If $$b$$ is a non-negative integer, $$P$$ satisfy the congruence $P \equiv b \pmod {9699690}$ Find the smallest value of $$b$$.

Details and Assumptions

• You may need to refer to list of primes as a reference.

• No computational aid is required in solving this problem.

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