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Let $\text{D}$ be a recurring decimal of the form, $\text{D} = 0.a_1a_2a_1a_2a_1a_2 \dots,$ where digits $a_1$ and $a_2$ lie between $0$ and $9.$ Further, at most one of them is zero. Then which of the following numbers necessarily produces an integer, when multiplied by $\text{D}?$

  1. $18$
  2. $108$
  3. $198$
  4. $288$
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