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In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose general fibre is a rational curve. If $r$ is the Cartier index of the fibre, it was expected that $12r$ would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in $r$, we provide a bound $N\left(r\right)$ and an example where the smallest integer that clears the denominators of the moduli part is $N\left(r\right)/r$. Moreover we prove that even locally the denominators depend...