\(14!\) can be written as \(14*13*12*11*10*9*8*7*6*5*4*3*2*1\)

Here we only need terms that are multiples of \(7\) so we have \(14\) and\(7\).

\(14\) can be rewritten as \(7 *2\) hence in this factorial we have \(7^2 * a\) ; where a is all the other remaining numbers multiplied together

Hence in the expression \(7^m\) m can acquire the maximum value of \(2\)

option B

Another approach is to divide the factorial number by the number in question whose power is to be raised

Therefore \(\frac{14}{7} = 2\)

\(2\) cannot be further divided by \(7\) hence \(m = 2\)

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes