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

 It is currently 06 Oct 2015, 16:16

### 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

# Events & Promotions

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

# The least common multiplier of A and B is 120, the ratio of

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
SVP
Joined: 28 Dec 2005
Posts: 1576
Followers: 2

Kudos [?]: 101 [0], given: 2

The least common multiplier of A and B is 120, the ratio of [#permalink]  09 Jan 2009, 19:52
3
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

75% (01:42) correct 25% (02:09) wrong based on 35 sessions
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The least common multiplier of A and B is 120, the ratio of A and B is 3:4, what is the largest common divisor?

Can someone break this down step by step for me ? I find that Im having some difficulty in understanding the concept behind these types of questions. Thanks in advance
Manager
Joined: 28 Jul 2004
Posts: 136
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
Followers: 1

Kudos [?]: 27 [0], given: 2

Re: PS: LCM [#permalink]  09 Jan 2009, 21:53
Tiger, I think your solution is not correct.

The problem says that LCM of a and b = 120 and from your calculations, a = 360 , b = 480.

How can the numbers be greater than their Least Common Multiple?

Here is my solution:

a x X = 120 (1)
b x Y = 120 (2)

Also, a/b = 3/4

Doing (1) / (2)

X/Y x 3/4 = 1 --> 3X = 4Y --> X = 4 and Y = 3 (I am taking the least possible values for X and Y)

From (1) , a x 4 = 120 --> a = 30
From (2), b x 3 = 120 --> b = 40

Therefore HCF of a and b = 10.
_________________

kris

Director
Joined: 01 Apr 2008
Posts: 903
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 19

Kudos [?]: 381 [0], given: 18

Re: PS: LCM [#permalink]  19 Jan 2009, 06:41
How do you get x= 4 and y=3 from the two equations? ( as the least possible values ?)
Manager
Joined: 28 Jul 2004
Posts: 136
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
Followers: 1

Kudos [?]: 27 [0], given: 2

Re: PS: LCM [#permalink]  28 Mar 2009, 20:08
Economist wrote:
How do you get x= 4 and y=3 from the two equations? ( as the least possible values ?)

3X = 4Y .. The equation holds good when X = 4 and Y =3 . With these values:

LHS = 3 x 4 =12
RHS = 4 x 3 = 12

---> LHS = RHS for X =4 and Y = 3.

Hope it is clear now.
_________________

kris

Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 11

Kudos [?]: 105 [20] , given: 0

Re: PS: LCM [#permalink]  29 Mar 2009, 05:28
20
This post received
KUDOS
6
This post was
BOOKMARKED
pmenon wrote:
The least common multiplier of A and B is 120, the ratio of A and B is 3:4, what is the largest common divisor?

Can someone break this down step by step for me ? I find that Im having some difficulty in understanding the concept behind these types of questions. Thanks in advance

Given LCM = 120 and the ratio of the numbers = 3:4. We need to find the GCD.

Let the numbers be 3x and 4x. So it is clear that their GCD = x.

We have,

$$LCM \times GCD = Product \quad of \quad the \quad two \quad numbers$$

$$\Rightarrow 120 \times x = 3x \times 4x$$

$$\Rightarrow x = 10$$

Hence the greatest common divisor is 10
_________________
Current Student
Joined: 04 Nov 2009
Posts: 78
Schools: NYU Stern '12
WE 1: Business Development
WE 2: Superhero- shhhhhh
Followers: 4

Kudos [?]: 16 [0], given: 10

Re: PS: LCM [#permalink]  01 Dec 2009, 00:11
Not sure if i did this correctly, but I got 10 as well.

120 broken down into its prime factors is 2^3 x 5 x 3

If the ratio is 3:4, the number must be divisible by 3, 4(2^2)
That leaves 2^1 x 5 in the prime factorization = 10

Any thoughts on this approach?
_________________

"Any school that meets you and still lets you in is not a good enough school to go to" - my mom upon hearing i got in
Thanks mom.

Manager
Joined: 04 Apr 2010
Posts: 165
Followers: 1

Kudos [?]: 103 [1] , given: 31

Re: PS: LCM [#permalink]  05 Apr 2010, 10:59
1
This post received
KUDOS
Hey Mustafaj,
Your approach is very correct and kind of logical too -compared to other apporaches.
Thanks,

mustafaj wrote:
Not sure if i did this correctly, but I got 10 as well.

120 broken down into its prime factors is 2^3 x 5 x 3

If the ratio is 3:4, the number must be divisible by 3, 4(2^2)
That leaves 2^1 x 5 in the prime factorization = 10

Any thoughts on this approach?

_________________

Consider me giving KUDOS, if you find my post helpful.
If at first you don't succeed, you're running about average. ~Anonymous

Senior Manager
Joined: 03 Nov 2005
Posts: 397
Location: Chicago, IL
Followers: 3

Kudos [?]: 32 [4] , given: 17

Re: PS: LCM [#permalink]  17 Aug 2010, 15:33
4
This post received
KUDOS
Very simple approach. No equations involved.

all the prime factors of 120: 2,3,4,5.

A:B=3:4 means that 2 and 5 are factors of both A and B

So, factors of A are 3,2,5 anf factors of B are 4,2,5.

looking at both, it is clear that 2 and 5 are factors of both, so LCD=5x2=10

E
_________________

Hard work is the main determinant of success

Intern
Joined: 18 Oct 2010
Posts: 3
Followers: 0

Kudos [?]: 3 [2] , given: 1

Re: PS: LCM [#permalink]  17 Nov 2010, 09:58
2
This post received
KUDOS
1
This post was
BOOKMARKED
Hello there everyone,

I'm not sure if anybody's still interested in this question, but I found the solutions posted earlier a bit tedious to think up in under two minutes.
This got me thinking a bit more deeper into what the question's actually telling; and here's how I reasoned an answer:

Given:
LCM (A,B) = 120
That bit's telling that for the two numbers A and B:

The [Common multiples between (A,B)] x [Uncommon multiples between them] = 120
That's the wordy definition of LCM right? Take out all that's common, and multiply them with whatever uncommon remains and you'll get the LCM between A and B

Now, what's worth noting in this equation is that the first part of it [Common multiples (A,B)] is simply their GCF;
So, 120 = GCF (A,B) x [Uncommon Factors of (A,B)]

I got this far in my thought process, and then gave up, because I thought there wasn't any information on what's uncommon between A,B..
But wait!
The question says that A/B = 3/4 ... that's as good as saying that 3 and 4 are the only factors that would remain if I divided A and B -- 3 and 4 are the Uncommon factors between A and B

So, using this bit of information, now you can solve for the GCF:

120 = GCF (A,B) x 3 x 4
120 = GCF x 12
GCF = 10

From this I realized something really simple but which was not obvious to me:

LCM / GCF = product of uncommon factors; if you are given the ratio between the numbers, then each value in the ratio is an uncommon factor belongs to one of the numbers
[i.e if two numbers are in the ratio 15:16, then their GCFx15x16 would give you their LCM]

Hope that helps!
Raj

ps: excuse me if you find any errors/ if i am not clear, but as you may notice below my username, this is my first post!
Intern
Joined: 27 Aug 2010
Posts: 30
Followers: 0

Kudos [?]: 3 [0], given: 4

Re: PS: LCM [#permalink]  20 Nov 2010, 14:44
Werewolf wrote:
peraspera wrote:
cicerone wrote:
The least common multiplier of A and B is 120, the ratio of A and B is 3:4, what is the largest common divisor?

Can someone break this down step by step for me ? I find that Im having some difficulty in understanding the concept behind these types of questions. Thanks in advance

Given LCM = 120 and the ratio of the numbers = 3:4. We need to find the GCD.

Let the numbers be 3x and 4x. So it is clear that their GCD = x.

We have,

$$LCM \times GCD = Product \quad of \quad the \quad two \quad numbers$$

$$\Rightarrow 120 \times x = 3x \times 4x$$

$$\Rightarrow x = 10$$

Hence the greatest common divisor is 10

Yup, I got there the same way.

Thanks for a smart and efficient way!

+1 , Thats indeed a smart way .
A concept can be used to solve this problem-
When you say LCM of A and B (for example A=3 and B=4 ) then we know for sure that the LCM of A and B (which is 120 here) will be divisible by both A and B ,that give us
no1= 120/A=120/3= 40 &
no2= 120/B=120/4 =30

GCF(40,30)= 10 .
_________________

This time , its my time .

Senior Manager
Status: 750+ or Burst !
Joined: 01 May 2011
Posts: 388
Location: India
Concentration: General Management, Strategy
GMAT 1: 670 Q48 V35
GPA: 3.5
Followers: 22

Kudos [?]: 79 [0], given: 26

Re: PS: LCM [#permalink]  22 May 2011, 06:24
pmenon wrote:
The least common multiplier of A and B is 120, the ratio of A and B is 3:4, what is the largest common divisor?

Can someone break this down step by step for me ? I find that Im having some difficulty in understanding the concept behind these types of questions. Thanks in advance

This can be solved using the principal of LCM X HCF = Product of the numbers.

LCM = 120

Ratio is 3:4. So let the numbers be 3x and 4x. Now, when we multiply numerator and denominator with x , the variable x becomes the HCF, thinking logically. Because cancelling the greatest factor we turn up to 3:4 which cannot be simplified further.

So finally we have

3x*4x = x*120 which gives x = 10. Ans : 10
_________________

GMAT done - a mediocre score but I still have a lot of grit in me

The last 20 days of my GMAT journey

Intern
Joined: 03 Sep 2010
Posts: 17
Followers: 0

Kudos [?]: 9 [0], given: 0

Re: PS: LCM [#permalink]  23 May 2011, 13:01
Let X be the highest common factor

So one number be 3X and the other is 4X

If there are two numbers , say 12 (3*4) and 28 (7*4) whose highest common factor/divisor is 4 , then the LCM is 3*7*4 = 84

Lets say another example , if there are two numbers , say 10 (5*2) and 14 (7*2)
Then the LCM is 5*7*2 = 70

Thus following the same logic in this question , 3 * 4 * X = 120

So X = 10

This could have been also solved by the concept of interpreting HCF and LCM using Venn Diagrams but i am unable to depict the diagram here

Hope this clears the problem
SVP
Joined: 16 Nov 2010
Posts: 1676
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 382 [1] , given: 36

Re: PS: LCM [#permalink]  23 May 2011, 21:54
1
This post received
KUDOS
A/B = 3/4

3 * GCD * 4 * GCD = 120 * GCD

=> GCD = 120/12 = 10
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 16 May 2011
Posts: 204
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE: Law (Law)
Followers: 1

Kudos [?]: 49 [0], given: 37

Re: PS: LCM [#permalink]  24 May 2011, 01:15
a=3*x
b= 4(2^2)*y
a*b= 3*2^3*5(120)*x*y (hence the factor will be less than x*y we can ignore the xy)

a has the 3 from 120 and b has the 2^2 from 120=hence-what's left from 120 is 2*5=10
Manager
Joined: 16 May 2011
Posts: 204
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE: Law (Law)
Followers: 1

Kudos [?]: 49 [0], given: 37

Re: PS: LCM [#permalink]  18 Jun 2011, 08:25
hope i got it right:
120x=4x*3x

120 is 2*2*2*3*5 the numbers ar 3/4 means 3/2*2 hence 2*5 will be the solution
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 6746
Followers: 365

Kudos [?]: 82 [0], given: 0

Re: The least common multiplier of A and B is 120, the ratio of [#permalink]  03 Oct 2013, 18:29
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 Club Legend
Joined: 09 Sep 2013
Posts: 6746
Followers: 365

Kudos [?]: 82 [0], given: 0

Re: The least common multiplier of A and B is 120, the ratio of [#permalink]  10 Nov 2014, 22:36
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.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 27

Kudos [?]: 1142 [0], given: 193

Re: The least common multiplier of A and B is 120, the ratio of [#permalink]  12 Nov 2014, 01:50
Ratio = $$\frac{3}{4}$$

LCM = 120 = 3 * 4 * 10

Just observe:

Ignore the numbers in ratio (3 & 4) They are already in LCM. What remains is 10

Answer = 10
_________________

Kindly press "+1 Kudos" to appreciate

Re: The least common multiplier of A and B is 120, the ratio of   [#permalink] 12 Nov 2014, 01:50
Similar topics Replies Last post
Similar
Topics:
3 Which of the following cannot be the least common multiple 4 06 Feb 2014, 02:24
3 Probability - Multiplying any # from A with any # in B 6 23 Apr 2010, 10:43
6 A strain of bacteria multiplies such that the ratio of its p 16 19 Feb 2010, 19:44
11 If the least common multiple of positive integer m and n is 11 12 Jun 2008, 23:09
15 If a and b are positive even integers, and the least common 6 11 Oct 2005, 17:32
Display posts from previous: Sort by

# The least common multiplier of A and B is 120, the ratio of

 Question banks Downloads My Bookmarks Reviews Important topics

 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®.