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By the [[unique factorization theorem]], any {{math | ''n'' > 1}} can be written in a unique way as
:<math> n= p_1^{r_1}p_2^{r_2} \cdots p_{k}^{r_k} </math>
where {{math | ''p''<sub>1</sub> < ''p''<sub>2</sub> < ... < ''p<sub>k</sub>''}} are [[Prime number|prime]]s and {{math | ''r''<sub>1</sub>, ''r''<sub>2</sub>, ..., ''r<sub>k</sub>''}} are positive integers. Then {{math | ''λ''(''n'')}} is the [[least common multiple]] of the {{mvar | λ}} of each of its prime power factors:
:<math>\lambda(n) = \operatorname{lcm}\Bigl(\lambda\left(p_1^{r_1}\right),\lambda\left(p_2^{r_2}\right),\ldots,\lambda\left(p_k^{r_k}\right)\Bigr).</math>
This can be proved using the [[Chinese remainder theorem]].
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