It is currently 19 Oct 2017, 09:41

### 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

# The LCM of three numbers is four times their GCF. Which of

Author Message
TAGS:

### Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 121

Kudos [?]: 1144 [1], given: 17

The LCM of three numbers is four times their GCF. Which of [#permalink]

### Show Tags

12 Mar 2013, 00:36
1
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:22) correct 46% (01:25) wrong based on 156 sessions

### HideShow timer Statistics

The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?

I. At least one of the numbers is odd.
II. Two of the three numbers must be same.
III. At least one number is the same as GCF.

A. I only
B. III only
C. I and III only
D. I and II only
E. II and III only
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Kudos [?]: 1144 [1], given: 17

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128870 [0], given: 12183

Re: The LCM of three numbers is four times their GCF. Which of [#permalink]

### Show Tags

12 Mar 2013, 06:42
emmak wrote:
The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?

I. At least one of the numbers is odd.
II. Two of the three numbers must be same.
III. At least one number is the same as GCF.

A. I only
B. III only
C. I and III only
D. I and II only
E. II and III only

Consider the following set: {2, 4, 8}.

GCF = 2.
LCM = 8 = 4*2.

The set discards options I and II. Only B fits.

_________________

Kudos [?]: 128870 [0], given: 12183

Intern
Joined: 02 Feb 2012
Posts: 29

Kudos [?]: 14 [0], given: 35

GPA: 4
Re: The LCM of three numbers is four times their GCF. Which of [#permalink]

### Show Tags

12 Mar 2013, 11:28
Hi Bunuel,

Is there any general approach to solve this problem??
Finding a set of 3 numbers might be difficult somtimes

Bunuel wrote:
emmak wrote:
The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?

I. At least one of the numbers is odd.
II. Two of the three numbers must be same.
III. At least one number is the same as GCF.

A. I only
B. III only
C. I and III only
D. I and II only
E. II and III only

Consider the following set: {2, 4, 8}.

GCF = 2.
LCM = 8 = 4*2.

The set discards options I and II. Only B fits.

Kudos [?]: 14 [0], given: 35

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17359 [5], given: 232

Location: Pune, India
Re: The LCM of three numbers is four times their GCF. Which of [#permalink]

### Show Tags

12 Mar 2013, 21:29
5
KUDOS
Expert's post
1
This post was
BOOKMARKED
avinashrao9 wrote:
Hi Bunuel,

Is there any general approach to solve this problem??
Finding a set of 3 numbers might be difficult somtimes

Consider a generic approach.
LCM - L
GCF - G
L = 4*G

The numbers must be of the form: Gn, Gm, Gk.
Since other than G, L contains only 4, n, m and k must be of one of the three numbers: 1, 2, 4

Mind you, there must be one number which is G because otherwise, the GCF will change. GCF of 2G, 2G, 4G will be 2G, not G.
There must be one number which is 4G because otherwise, the LCM will change. LCM of G, 2G, 2G is 2G, not 4G

So the three numbers could be of the form:
G, 2G, 4G or
G, G, 4G or
G, 4G, 4G

If G is even, no number will be odd.
Hence I and II needn't be true. III must be true.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17359 [5], given: 232

Intern
Joined: 27 Dec 2012
Posts: 41

Kudos [?]: 15 [0], given: 11

Re: The LCM of three numbers is four times their GCF. Which of [#permalink]

### Show Tags

27 Mar 2013, 14:09
VeritasPrepKarishma wrote:
avinashrao9 wrote:
Hi Bunuel,

Is there any general approach to solve this problem??
Finding a set of 3 numbers might be difficult somtimes

Consider a generic approach.
LCM - L
GCF - G
L = 4*G

The numbers must be of the form: Gn, Gm, Gk.
Since other than G, L contains only 4, n, m and k must be of one of the three numbers: 1, 2, 4

Mind you, there must be one number which is G because otherwise, the GCF will change. GCF of 2G, 2G, 4G will be 2G, not G.
There must be one number which is 4G because otherwise, the LCM will change. LCM of G, 2G, 2G is 2G, not 4G

So the three numbers could be of the form:
G, 2G, 4G or
G, G, 4G or
G, 4G, 4G

If G is even, no number will be odd.
Hence I and II needn't be true. III must be true.

Hi karishma,
I could not understand anything out of this explanation. Could you please explain it to me in a more detailed manner??

Kudos [?]: 15 [0], given: 11

Current Student
Joined: 06 Sep 2013
Posts: 1978

Kudos [?]: 719 [0], given: 355

Concentration: Finance
Re: The LCM of three numbers is four times their GCF. Which of [#permalink]

### Show Tags

25 Dec 2013, 16:34
Bunuel wrote:
emmak wrote:
The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?

I. At least one of the numbers is odd.
II. Two of the three numbers must be same.
III. At least one number is the same as GCF.

A. I only
B. III only
C. I and III only
D. I and II only
E. II and III only

Consider the following set: {2, 4, 8}.

GCF = 2.
LCM = 8 = 4*2.

The set discards options I and II. Only B fits.

Is there any algebraic/conceptual approach to this question Bunuel?

Thanks
Cheers!

J

Kudos [?]: 719 [0], given: 355

Intern
Joined: 22 Nov 2013
Posts: 4

Kudos [?]: 3 [0], given: 0

Re: The LCM of three numbers is four times their GCF. Which of [#permalink]

### Show Tags

25 Dec 2013, 18:28
1
This post was
BOOKMARKED
Jlgdr,

I guess what Karishma is saying is this :

G*N, G*M, G*K are the 3 numbers whose GCF is G. LCM of these 3 numbers can be written as
LCM(G*N,G*M,G*K) = G*LCM(N,M,K) = 4 *G (given). So LCM(N,M,K) = 4. This would mean {N,M,K} can be {1,1,4} or {1,2,4} or {1,4,4} since the LCM of the 3 numbers is 4.
So the only possible solution is number B.

Kudos [?]: 3 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16673

Kudos [?]: 273 [0], given: 0

Re: The LCM of three numbers is four times their GCF. Which of [#permalink]

### Show Tags

15 Sep 2017, 03:54
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: The LCM of three numbers is four times their GCF. Which of   [#permalink] 15 Sep 2017, 03:54
Display posts from previous: Sort by