Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 29 Aug 2005
Posts: 255

If the least common multiple of positive integer m and n is
[#permalink]
Show Tags
Updated on: 20 Oct 2013, 23:12
Question Stats:
61% (01:45) correct 39% (02:13) wrong based on 440 sessions
HideShow timer Statistics
If the least common multiple of positive integer m and n is 120, and m:n=3:4, what is the greatest common factor of m and n? (A) 3 (B) 5 (C) 6 (D) 10 (E) 12
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
The world is continuous, but the mind is discrete
Originally posted by vd on 13 Jun 2008, 00:09.
Last edited by Bunuel on 20 Oct 2013, 23:12, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.




CEO
Joined: 17 Nov 2007
Posts: 3446
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: If the least common multiple of a positive integer
[#permalink]
Show Tags
13 Jun 2008, 06:37
Dfist way: LCM=120=3*2^3*5 1. LCM contains prime number 5, so m or n or both also contain 5. 2. if m:n=3:4 then only both m and m contain 5. Therefore, GCD is 5 or 10. 3. LCM contains 2^3, but in ratio m:n we have only 4=2^2. So, both m and m contain 2. GCD=10. second way: m*n=LCM*GCD  it is a formula. m*n=3x*4x=120*GCD > GCD=x^2/10 > only 10 works.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  Limited GMAT/GRE Math tutoring in Chicago




SVP
Joined: 04 May 2006
Posts: 1692
Schools: CBS, Kellogg

Re: If the least common multiple of a positive integer
[#permalink]
Show Tags
13 Jun 2008, 00:26
vdhawan1 wrote: If the least common multiple of a positive integer m and n is 120 and m:n is 3:4 what is the greatest common factor of m and n
3 5 6 10 12
Please provide detailed explanations on how to solve this
many thanks D for me! x is the least common factor of m and n m*n=3x*4x=120*x, so x=10, because x can not be 0!
_________________
GMAT Club Premium Membership  big benefits and savings



Current Student
Joined: 12 Jun 2008
Posts: 286
Schools: INSEAD Class of July '10

Re: If the least common multiple of a positive integer
[#permalink]
Show Tags
13 Jun 2008, 04:56
sondenso wrote: D for me! x is the least common factor of m and n m*n=3x*4x I don't get this (where does it come from ?) sondenso wrote: 3x*4x=120*x This is just false sondenso wrote: =120*x, so x=10, because x can not be 0! I don't get this either. Can you explain ?



Current Student
Joined: 12 Jun 2008
Posts: 286
Schools: INSEAD Class of July '10

Re: If the least common multiple of a positive integer
[#permalink]
Show Tags
13 Jun 2008, 06:45
walker wrote: D
fist way:
LCM=120=3*2^3*5
1. LCM contains prime number 5, so m or n or both also contain 5. 2. if m:n=3:4 then only both m and m contain 5. Therefore, GCD is 5 or 10. 3. LCM contains 2^3, but in ratio m:n we have only 4=2^2. So, both m and m contain 2. GCD=10. I like this. Thanks ! walker wrote: second way:
m*n=LCM*GCD  it is a formula. m*n=3x*4x=120*GCD > GCD=x^2/10 > only 10 works. Thanks for the refresh on the formula, I did not remember. But why is m*n = 3x*4x ?



CEO
Joined: 17 Nov 2007
Posts: 3446
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: If the least common multiple of a positive integer
[#permalink]
Show Tags
13 Jun 2008, 06:48
Oski wrote: But why is m*n = 3x*4x ? m:n=3:4 > m=3x, n=4x where x is an integer (m/n=3x/4x=3/4)
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  Limited GMAT/GRE Math tutoring in Chicago



Current Student
Joined: 12 Jun 2008
Posts: 286
Schools: INSEAD Class of July '10

Re: If the least common multiple of a positive integer
[#permalink]
Show Tags
13 Jun 2008, 06:53
walker wrote: Oski wrote: But why is m*n = 3x*4x ? m:n=3:4 > m=3x, n=4x where x is an integer (m/n=3x/4x=3/4) Yes, sure, but why is this x necessarily the GCD ? Edit : Okay, I got it. This is because there is no common divisors in 3 and 4... (I guess this should be part of the demonstration ^^)



Manager
Joined: 26 Sep 2013
Posts: 197
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: If the least common multiple of a positive integer m and n
[#permalink]
Show Tags
20 Oct 2013, 16:04
vd wrote: If the least common multiple of a positive integer m and n is 120 and m:n is 3:4 what is the greatest common factor of m and n
3 5 6 10 12
Please provide detailed explanations on how to solve this
many thanks I just plugged in numbers for m & n. If the ratio is 3:4, then using 3 & 4 for their values works fine, since we're trying to find the GCF, and not the actual values of m&n, so m*n=LCM*GCF 3*4=120*GCF 12=120*GCF 10=GCF D.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12673
Location: United States (CA)

Re: If the least common multiple of positive integer m and n is
[#permalink]
Show Tags
12 Jan 2015, 16:29
Hi All, There are a number of different ways to approach this question. Given the "restrictions" that are in the prompt, if you're not sure what to do with a question such as this, you can always "brute force" it.... 'Brute Force' is essentially just throwing numbers at a situation until you find the correct answer (or at least find the pattern that will lead you to the correct answer). It's not particularly elegant, but in the right circumstances it can be a really fast way to get to the correct answer. In this question, we're told: 1) M and N are positive integers 2) The LCM of M and N is 120 3) The ratio of M:N is 3:4 I'm going to focus on how the second and third "restrictions" interact.... If M=3 and N=4, then the LCM would be 12 (not 120). Notice the "times 10" difference?.... What if... M = 30 and N = 40. Multiples of 30: 30, 60, 90, 120 Multiples of 40: 40, 80, 120 The LCM IS 120. With 30 and 40 as our two values, it's not hard to find the GREATEST common factor. It has to be 10. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If the least common multiple of positive integer m and n is
[#permalink]
Show Tags
12 Jan 2015, 23:41
m:n = 3:4 \(m = \frac{120}{4} = 30\) \(n = \frac{120}{3} = 40\) GCD of 30 & 40 = 10 Answer = D
_________________
Kindly press "+1 Kudos" to appreciate



Director
Joined: 23 Jan 2013
Posts: 575

If the least common multiple of positive integer m and n is
[#permalink]
Show Tags
21 Sep 2015, 00:25
120=5*2*3*2*2
3/4 means 3 and 2*2 in two numbers exist, so we should give another 2*5 to both numbers to get the same ratio
3*5*2/2*2*2*5=30/40
GCF=10
D



Manager
Joined: 09 Jun 2015
Posts: 94

Re: If the least common multiple of positive integer m and n is
[#permalink]
Show Tags
14 Mar 2016, 05:28
vd wrote: If the least common multiple of positive integer m and n is 120, and m:n=3:4, what is the greatest common factor of m and n?
(A) 3 (B) 5 (C) 6 (D) 10 (E) 12 Supposing that m and n are 3*x and 4*x; LCM of m and n = 12*x= 120=>x=10 Since 3 and 4 are coprime numbers 10 must be the gcf.



Current Student
Joined: 12 Aug 2015
Posts: 2638

Re: If the least common multiple of positive integer m and n is
[#permalink]
Show Tags
26 Nov 2016, 07:57
Nice Question. Here is what i did => As m/n=3/4 Let m=3x n=4x Now GCD = Common elements => x LCM=common elements *leftovers => x*3*4=> 12x Hence !2x=120 so x=10 Hence GCD=10 Hence D Additionally we can say that numbers m and n must be 30 and 40
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3864
Location: United States (CA)

Re: If the least common multiple of positive integer m and n is
[#permalink]
Show Tags
07 Jul 2018, 18:33
vd wrote: If the least common multiple of positive integer m and n is 120, and m:n=3:4, what is the greatest common factor of m and n?
(A) 3 (B) 5 (C) 6 (D) 10 (E) 12 We can let m = 3x and n = 4x for some positive integer x. We see that since 3 and 4 have no common factor (other than 1), the least common multiple (LCM) of m and n must be (3)(4)(x). Since it’s given that the LCM is 120, we have: (3)(4)(x) = 120 12x = 120 x = 10 So m = 30 and n = 40, and we see that 10 is the greatest common factor of m and n. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: If the least common multiple of positive integer m and n is &nbs
[#permalink]
07 Jul 2018, 18:33






