If the least common multiple of positive integer m and n is : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 19 Feb 2017, 08:41

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 29 Aug 2005
Posts: 283
Followers: 2

Kudos [?]: 55 [0], given: 0

If the least common multiple of positive integer m and n is [#permalink]

### Show Tags

12 Jun 2008, 23:09
8
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

60% (02:16) correct 40% (01:37) wrong based on 374 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
[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
Joined: 04 May 2006
Posts: 1925
Schools: CBS, Kellogg
Followers: 23

Kudos [?]: 1040 [0], given: 1

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!
_________________
Current Student
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 7

Kudos [?]: 52 [0], given: 0

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: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 556

Kudos [?]: 3651 [1] , given: 360

Re: If the least common multiple of a positive integer [#permalink]

### Show Tags

13 Jun 2008, 05:37
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
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
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 7

Kudos [?]: 52 [0], given: 0

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: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 556

Kudos [?]: 3651 [0], given: 360

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

Current Student
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 7

Kudos [?]: 52 [0], given: 0

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: 221
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 4

Kudos [?]: 145 [2] , given: 40

Re: If the least common multiple of a positive integer m and n [#permalink]

### Show Tags

20 Oct 2013, 15:04
2
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.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13869
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: If the least common multiple of positive integer m and n is [#permalink]

### Show Tags

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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8513
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 395

Kudos [?]: 2548 [3] , given: 164

Re: If the least common multiple of positive integer m and n is [#permalink]

### Show Tags

12 Jan 2015, 15:29
3
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.

[Reveal] Spoiler:
D

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

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point 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: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 49

Kudos [?]: 1980 [1] , given: 193

Re: If the least common multiple of positive integer m and n is [#permalink]

### Show Tags

12 Jan 2015, 22:41
1
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

_________________

Kindly press "+1 Kudos" to appreciate

Director
Joined: 23 Jan 2013
Posts: 582
Schools: Cambridge'16
Followers: 1

Kudos [?]: 21 [0], given: 40

If the least common multiple of positive integer m and n is [#permalink]

### Show Tags

20 Sep 2015, 23:25
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: 101
Followers: 0

Kudos [?]: 4 [0], given: 0

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 co-prime numbers 10 must be the gcf.
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1926
Followers: 59

Kudos [?]: 418 [0], given: 476

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
_________________

Give me a hell yeah ...!!!!!

Re: If the least common multiple of positive integer m and n is   [#permalink] 26 Nov 2016, 06:57
Similar topics Replies Last post
Similar
Topics:
3 m and n are positive integers. 2 09 Dec 2016, 00:54
11 The greatest common factor of positive integers m and n is 12. What is 5 08 Jul 2015, 02:43
10 If the least common multiple of a positive integer x ,4^3 and 6^5 is 6 3 04 Dec 2014, 01:46
9 The least common multiple of positive integer m and 3-digit 7 23 Nov 2013, 01:42
1 If N is the least positive integer that is a multiple of 5 26 Nov 2012, 23:58
Display posts from previous: Sort by