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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## n is a product of 6 distinct prime numbers. m!/n is an integ tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 1 member reply ### GMAT/MBA Expert ## n is a product of 6 distinct prime numbers. m!/n is an integ ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] n is a product of 6 distinct prime numbers. m!/n is an integer. What is the smallest possible value of m? A. 10 B. 11 C. 12 D. 13 E. 14 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$99 for 3 month Online Course
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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

n is a product of 6 distinct prime numbers. m!/n is an integer.
What is the smallest possible value of m?

A. 10
B. 11
C. 12
D. 13
E. 14
$$\left. \matrix{ n = {p_1} \cdot {p_2} \cdot \ldots \cdot {p_6}\,\,\,{\rm{primes}}\,\,{\rm{and}}\,\,{\rm{distincts}}\,\,\, \hfill \cr {{m!} \over n} = {\mathop{\rm int}} \hfill \cr ? = m\,\,\min \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{Take}}\,\,\left( {{p_1},{p_2},{p_3},{p_4},{p_5},{p_6}} \right) = \left( {2,3,5,7,11,13} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 13$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Smallest 6 prime numbers = 2, 3, 5, 7, 11, 13

So, m! should include all of them.

Implies smallest possible value of m = 13

Therefore, the correct answer is D

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The smallest product of 6 distinct prime numbers is n = 2*3*5*7*11*13. 13! Is the smallest factorial that is divisible by 2*3*5*7*11*13. Thus, the smallest possible integer value of m is 13.

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Only $99 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1795 messages Followed by: 14 members Upvotes: 43 Max@Math Revolution wrote: [Math Revolution GMAT math practice question] n is a product of 6 distinct prime numbers. m!/n is an integer. What is the smallest possible value of m? A. 10 B. 11 C. 12 D. 13 E. 14 The smallest product of 6 distinct prime numbers is: 2 x 3 x 5 x 7 x 11 x 13, so we see that m! must have a prime of 13, so the least value of m is 13. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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