The product of first twelve positive integers is divisible by all of the the following EXCEPT?  Options
A) 210 B) 88 C) 75 D) 60 E) 34
The product of the first twelve positive integers, 12!12! contains only the primes less than 12 (2, 3, 5, 7, 11), which means that the product won't be divisible by any number containing higher prime number.   Now, you can notice that 34= 2*17= 
<gadget id="calculator"> 2*17</gadget>
<output>34</output>
34 too.   Answer: 34.
<result>E</result>
The product of first twelve positive integers is divisible by all of the the following EXCEPT?