Modulo makes it weak

Number Theory Level 3

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.