Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 29 Aug 2005
Posts: 272

If the least common multiple of positive integer m and n is [#permalink]
Show Tags
12 Jun 2008, 23:09
10
This post was BOOKMARKED
Question Stats:
63% (01:18) correct 37% (01:38) wrong based on 388 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
Last edited by Bunuel on 20 Oct 2013, 22:12, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.



SVP
Joined: 04 May 2006
Posts: 1877
Schools: CBS, Kellogg

Re: If the least common multiple of a positive integer [#permalink]
Show Tags
12 Jun 2008, 23:26
2
This post was BOOKMARKED
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: 287
Schools: INSEAD Class of July '10

Re: If the least common multiple of a positive integer [#permalink]
Show Tags
13 Jun 2008, 03:56
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 ?



CEO
Joined: 17 Nov 2007
Posts: 3583
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, 05:37
1
This post received KUDOS
Expert's post
4
This post was BOOKMARKED
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+  PrepGame



Current Student
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10

Re: If the least common multiple of a positive integer [#permalink]
Show Tags
13 Jun 2008, 05:45
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: 3583
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, 05:48
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+  PrepGame



Current Student
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10

Re: If the least common multiple of a positive integer [#permalink]
Show Tags
13 Jun 2008, 05:53
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: 216
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, 15:04
2
This post received KUDOS
2
This post was BOOKMARKED
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: 11058
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If the least common multiple of positive integer m and n is [#permalink]
Show Tags
12 Jan 2015, 15:29
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: 1839
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, 22:41
1
This post received KUDOS
1
This post was BOOKMARKED
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: 601

If the least common multiple of positive integer m and n is [#permalink]
Show Tags
20 Sep 2015, 23:25
1
This post received KUDOS
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: 102

Re: If the least common multiple of positive integer m and n is [#permalink]
Show Tags
14 Mar 2016, 04:28
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.



Retired Moderator
Joined: 12 Aug 2015
Posts: 2423
GRE 1: 323 Q169 V154

Re: If the least common multiple of positive integer m and n is [#permalink]
Show Tags
26 Nov 2016, 06:57
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
_________________
Getting into HOLLYWOOD with an MBA Stone Cold's Mock Tests for GMATQuant(700+)



NonHuman User
Joined: 09 Sep 2013
Posts: 13802

Re: If the least common multiple of positive integer m and n is [#permalink]
Show Tags
26 Jan 2018, 11:36
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If the least common multiple of positive integer m and n is
[#permalink]
26 Jan 2018, 11:36






