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Answer = D = 61

13!12! + 13!14!

= 13!12! + 13! * 14 * 13 * 12!

= 13!12!(1 + 169+13)

= 13! 12! * 61 * 3

GCD = 61
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(13!12!) + (13!14!)
13!12! x ( 1+ 14 x 13)
13!12! x 183
13!12! x 3 x 61
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Great Question
Here is what i did
N=12!*13![1+14*13]
N=12!*13!*183
N=12!*13!*3*61
61=> Prime Number
Hence greatest Prime is 61

Hence D
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