**Que:**If both 11 and \(7^2\) are factors of \(a\cdot4^5\cdot6^3\cdot7\), then what is the smallest possible value of a?

(A) 7

(B) 11

(C) 49

(D) 77

(E) 539

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**A**

**B**

**C**

**D**

**E**

(A) 7

(B) 11

(C) 49

(D) 77

(E) 539

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For 11 to be the factor it should be contained in it. If we remove ‘a’ then we don’t have 11. Hence a = 11.

=> 7 is contained already and hence we need 1 more 7 so that \(7^2\) is the factor and hence 7 should also be in a.

Thus, smallest value of a = 7 * 11 = 77

Answer D

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