If P represents the product of the first 15 positive integers, then P is not a multiple of:

A. 99
B. 84
C. 72
D. 65
E. 57
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Let’s look at the answer choices.

Since 99 = 9 x 11, both of which are included in the product of the first 15 integers, we see that P is a multiple of 99.

Similarly, since 84 = 42 x 2 = 21 x 4 = 7 x 3 x 4, we see that P is a multiple of 84.

Since 72 = 36 x 2 = 6 x 3 x 2 x 2 = 6 x 3 x 4, we see that P is a multiple of 72.

Since 65 = 5 x 13, we see that P is a multiple of 65.

Since 57 = 19 x 3, and since the product of the first 15 integers does not have a prime factor of 19, P cannot be a multiple of 57.

Answer: E
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Lets have a look at the answer choices-
A. 99 - 9X11- both are in P
B. 84 - 7X12- both are in P
C. 72 - 7X8- both are in P
D. 65 - 5X13- both are in P
E. 57 - 3X19

19 is a prime number and not there in the product- P.
The correct answer is E