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Find the smallest number when it is multiplied by 392 , then the product is perfect cube.

(a) 3

(b) 5

(c) 6

(d) 7

Solution:

\begin{aligned} \begin{array}{r|l} 2 & 392 \\ \hline 2 & 196 \\ \hline 2 & 98 \\ \hline 7 & 49 \\ \hline & 7 \\ \therefore \quad 392= & 2 \times 2 \times 2 \times 7 \times 7 \\ = & (2)^{3} \times 7 \times 7 \end{array} \end{aligned}

$\therefore$ The required no. $=7$; Ans.

Therefore, the correct option is (D)

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