$O_{KL} \subset \frac{1}{d}O_KO_L$ where $d = \text{gcd}(disc(O_K),disc(O_L))$

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Let $L,K$ be number fields such that $L\cap K =\mathbb{Q}$ then $O_{KL} \subset \frac{1}{d}O_KO_L$ where $d = \text{gcd}(disc(O_K),disc(O_L))$