Given that \(1^2 + 2^2 + 3^2 + \ldots + k^2 = \frac{k(k+1)(2k+1)}{6}\), what is the smallest integer \(k\) such that \(1^2 + 2^2 + 3^2 + \ldots + k^2\) is divisible by \(100\)?

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