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## Irrational number

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Tolaso J Kos
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### Irrational number

$\newcommand{\lcm}{{\rm lcm}}$ Let $\lcm$ denote the least common divisor. Prove that the number:

$$\mathcal{I}=\sum_{n=1}^{\infty} \frac{1}{\lcm (1, 2, \dots, n)}$$

is irrational.
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