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# A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6823
GMAT 1: 760 Q51 V42
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A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre  [#permalink]

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28 Oct 2018, 23:58
00:00

Difficulty:

5% (low)

Question Stats:

84% (00:35) correct 16% (00:46) wrong based on 58 sessions

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[Math Revolution GMAT math practice question]

A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 children with no pencils left over. What is the smallest possible number of pencils in the set?

A. 6
B. 12
C. 15
D. 30
E. 60

_________________

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" Intern Joined: 17 Nov 2016 Posts: 10 Re: A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre [#permalink] ### Show Tags 29 Oct 2018, 00:00 IMO E. LCM is the smallest possible number. So LCM of given no.s is 60 Posted from my mobile device Intern Joined: 12 Sep 2017 Posts: 3 Re: A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre [#permalink] ### Show Tags 29 Oct 2018, 04:30 shashaankbhat wrote: IMO E. LCM is the smallest possible number. So LCM of given no.s is 60 Posted from my mobile device Can you explain process? Intern Joined: 17 Nov 2016 Posts: 10 Re: A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre [#permalink] ### Show Tags 29 Oct 2018, 06:58 The smallest number which is evenly divisible by numbers 2, 3, 4, 5 and 6 is 60 which is the LCM. LCM can be found by using prime factorization method Ritace Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4351 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre [#permalink] ### Show Tags 29 Oct 2018, 07:53 Ritace Alternatively check using the option (A) Not divisible by 4 & 5 (B) Not divisible by 5 (C) Not divisible by 2 , 4 & 6 (D) Not divisible by 4 (E) Divisible by all the numbers... Hence, Answer must be (E) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4557 Location: United States (CA) Re: A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre [#permalink] ### Show Tags 30 Oct 2018, 18:10 MathRevolution wrote: [Math Revolution GMAT math practice question] A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 children with no pencils left over. What is the smallest possible number of pencils in the set? A. 6 B. 12 C. 15 D. 30 E. 60 We need to determine the LCM of 2, 3, 4, 5 and 6. Breaking each number into its prime factors, we have: 2 = 2 3 = 3 4 = 2^2 5 = 5 6 = 2 x 3 Thus, the LCM is 2^2 x 3 x 5 = 60. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6823 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre [#permalink] ### Show Tags 31 Oct 2018, 01:35 => The smallest possible number of pencils must be the least common multiple of $$2, 3, 4, 5$$and $$6$$. $$2 = 2^1, 3 = 3^1, 4 = 2^2, 5 = 5^1$$ and $$6 = 2^1*3^1.$$ We multiply the maximum powers of each base to obtain the least common multiple $$2^2*3^1*5^1 = 60.$$ Therefore, the answer is E. Answer: E _________________ 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: A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre &nbs [#permalink] 31 Oct 2018, 01:35
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# A set of pencils can be evenly shared between 2, 3, 4, 5 and 6 childre

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