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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

09 Jan 2009, 20:52

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

75% (00:42) correct
25% (02:09) wrong based on 55 sessions

HideShow timer Statistics

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

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
_________________

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!

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

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

Re: The least common multiplier of A and B is 120, the ratio of [#permalink]

Show Tags

03 Oct 2013, 19:29

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.
_________________

Re: The least common multiplier of A and B is 120, the ratio of [#permalink]

Show Tags

10 Nov 2014, 23:36

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.
_________________

Re: The least common multiplier of A and B is 120, the ratio of [#permalink]

Show Tags

28 Nov 2015, 13:39

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.
_________________

Re: The least common multiplier of A and B is 120, the ratio of [#permalink]

Show Tags

19 Feb 2017, 04:10

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.
_________________