If $a, b, c$ are distinct positive numbers, each different from $1$, such that $[{\log _b}a{\log _c}a - {\log _a}a] + [{\log _a}b{\log _c}b - {\log _b}b]$ $ + [{\log _a}c{\log _b}c - {\log _c}c] = 0,$ then $abc =$

  • A

    $1$

  • B

    $2$

  • C

    $3$

  • D

    None of these

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  • [JEE MAIN 2020]