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 350,000 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:

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

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

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

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

Re: If the least common multiple of positive integer m and n is [#permalink]
12 Jan 2015, 15:29

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.

safe.txmblr Can business make a difference in the great problems that we face? My own view is nuanced. I think business potentially has a significant role to play...

Still 7 months to go to be at Lausanne. But, as Lausanne has a vacancy rate of 0.1% for rental properties, I booked my rental apartment yesterday for...