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# n is a product of 6 distinct prime numbers. m!/n is an integer.

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82
n is a product of 6 distinct prime numbers. m!/n is an integer.  [#permalink]

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11 Jan 2019, 03:49
00:00

Difficulty:

35% (medium)

Question Stats:

68% (00:43) correct 32% (01:23) wrong based on 57 sessions

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[Math Revolution GMAT math practice question]

$$n$$ is a product of $$6$$ distinct prime numbers. $$\frac{m!}{n}$$ is an integer.
What is the smallest possible value of $$m$$?

$$A. 10$$
$$B. 11$$
$$C. 12$$
$$D. 13$$
$$E. 14$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Joined: 18 Aug 2017 Posts: 1253 Location: India Concentration: Sustainability, Marketing WE: Marketing (Energy and Utilities) Re: n is a product of 6 distinct prime numbers. m!/n is an integer. [#permalink] ### Show Tags 11 Jan 2019, 04:26 MathRevolution wrote: [Math Revolution GMAT math practice question] $$n$$ is a product of $$6$$ distinct prime numbers. $$\frac{m!}{n}$$ is an integer. What is the smallest possible value of $$m$$? $$A. 10$$ $$B. 11$$ $$C. 12$$ $$D. 13$$ $$E. 14$$ n = 2* 3*5*7*11*13 so m!/n can be an integer only when m = 13 ! IMO D _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Manager Joined: 01 May 2017 Posts: 69 Location: India Re: n is a product of 6 distinct prime numbers. m!/n is an integer. [#permalink] ### Show Tags 11 Jan 2019, 04:26 n is a product of 6 distinct prime numbers. m!/n is an integer. What is the smallest possible value of m? Smallest 6 prime numbers = 2,3,5,7,11,,13 So m! should include all of them implies smallest possible value of m = 13 Option D is correct Manager Joined: 18 Oct 2018 Posts: 51 Location: India Concentration: Finance, International Business GPA: 4 WE: Business Development (Retail Banking) Re: n is a product of 6 distinct prime numbers. m!/n is an integer. [#permalink] ### Show Tags 11 Jan 2019, 10:30 m!/n is an integer. For the value of n to be minimum, m!/n should be minimum. But since n is a product of 6 distinct prime no.'s, the minimum value of n=2*3*5*7*11*13 So, the minimum value of m such that m!/n is an integer is 13 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: n is a product of 6 distinct prime numbers. m!/n is an integer. [#permalink] ### Show Tags 13 Jan 2019, 17:04 => 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 $$13$$. Therefore, the answer is D. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: n is a product of 6 distinct prime numbers. m!/n is an integer.  [#permalink]

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14 Jan 2019, 18:03
MathRevolution wrote:
[Math Revolution GMAT math practice question]

$$n$$ is a product of $$6$$ distinct prime numbers. $$\frac{m!}{n}$$ 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.

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Re: n is a product of 6 distinct prime numbers. m!/n is an integer. &nbs [#permalink] 14 Jan 2019, 18:03
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