Find all School-related info fast with the new School-Specific MBA Forum

It is currently 02 Aug 2015, 04:43
GMAT Club Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the least common multiple of positive integer m and n is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 29 Aug 2005
Posts: 283
Followers: 1

Kudos [?]: 31 [0], given: 0

If the least common multiple of positive integer m and n is [#permalink] New post 12 Jun 2008, 23:09
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (02:21) correct 39% (01:53) wrong based on 171 sessions
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
[Reveal] Spoiler: OA

_________________

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
SVP
avatar
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
Followers: 19

Kudos [?]: 500 [0], given: 1

Premium Member
Re: If the least common multiple of a positive integer [#permalink] New post 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
User avatar
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 6

Kudos [?]: 41 [0], given: 0

Re: If the least common multiple of a positive integer [#permalink] New post 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 ?
Expert Post
1 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 424

Kudos [?]: 2295 [1] , given: 359

GMAT ToolKit User Premium Member
Re: If the least common multiple of a positive integer [#permalink] New post 13 Jun 2008, 05:37
1
This post received
KUDOS
Expert's post
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.

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 must-have app especially if you aim at 700+ | PrepGame

Current Student
User avatar
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 6

Kudos [?]: 41 [0], given: 0

Re: If the least common multiple of a positive integer [#permalink] New post 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 ?
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 424

Kudos [?]: 2295 [0], given: 359

GMAT ToolKit User Premium Member
Re: If the least common multiple of a positive integer [#permalink] New post 13 Jun 2008, 05:48
Expert's post
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 must-have app especially if you aim at 700+ | PrepGame

Current Student
User avatar
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 6

Kudos [?]: 41 [0], given: 0

Re: If the least common multiple of a positive integer [#permalink] New post 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 ^^)
1 KUDOS received
Current Student
avatar
Joined: 26 Sep 2013
Posts: 229
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 62 [1] , given: 40

Re: If the least common multiple of a positive integer m and n [#permalink] New post 20 Oct 2013, 15:04
1
This post received
KUDOS
1
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.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5711
Followers: 323

Kudos [?]: 63 [0], given: 0

Premium Member
Re: If the least common multiple of positive integer m and n is [#permalink] New post 12 Jan 2015, 00:46
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

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 3078
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 134

Kudos [?]: 852 [1] , given: 54

Re: If the least common multiple of positive integer m and n is [#permalink] New post 12 Jan 2015, 15:29
1
This post received
KUDOS
Expert's post
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:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich
_________________

Official Guide 2016 Question Breakdown:
http://gmatclub.com/forum/empowergmat-blog-198415.html#p1527977

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

GMAT Club Verified Reviews for EMPOWERgmat & Special Discount

EMPOWERgmat Podcast - A Wild Secret About The GMAT Algorithm


1 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1859
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 23

Kudos [?]: 1014 [1] , given: 193

Re: If the least common multiple of positive integer m and n is [#permalink] New post 12 Jan 2015, 22:41
1
This post received
KUDOS
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 :)

Re: If the least common multiple of positive integer m and n is   [#permalink] 12 Jan 2015, 22:41
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic The greatest common factor of positive integers m and n is 12. What is Bunuel 4 08 Jul 2015, 02:43
3 Experts publish their posts in the topic If the least common multiple of a positive integer x ,4^3 and 6^5 is 6 anceer 2 04 Dec 2014, 01:46
4 Experts publish their posts in the topic The least common multiple of positive integer m and 3-digit honchos 5 23 Nov 2013, 01:42
1 Experts publish their posts in the topic If N is the least positive integer that is a multiple of saxenarahul021 5 26 Nov 2012, 23:58
13 Experts publish their posts in the topic If a and b are positive even integers, and the least common vikramm 6 11 Oct 2005, 17:32
Display posts from previous: Sort by

If the least common multiple of positive integer m and n is

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.