Last visit was: Sat Sep 12, 2026 3:15 am It is currently Sat Sep 12, 2026 3:15 am
Home
Messages
Tests
Schools
Events
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
PyjamaScientist
User avatar
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Last visit: 14 Jul 2026
Posts: 1,123
Own Kudos:
1,396
 [38]
Given Kudos: 633
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Products:
My Reviews
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Posts: 1,123
Kudos: 1,396
 [38]
If M and N are two positive integers such that 7 times M is Sat Aug 28, 2021 4:38 am
2
Kudos
Add Kudos
36
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

69% (02:28) correct 31% (02:40) wrong based on 582 sessions

History

Date
Time
Result
Not Attempted Yet
If M and N are two positive integers such that 7 times M is 9 times N and 1260 is the least number that is a multiple of both M and N, then which among the following is the greatest number that can divide both M and N ?

(a) 20
(b) 30
(c) 40
(d) 50
(e) 60
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
Vetrick
User avatar
Joined: 19 Jul 2021
Last visit: 10 Dec 2022
Posts: 45
Own Kudos:
70
 [11]
Given Kudos: 30
Location: India
Posts: 45
Kudos: 70
 [11]
If M and N are two positive integers such that 7 times M is Sat Aug 28, 2021 10:22 pm
10
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
7M=9N

1260 = 7 * 2^2 * 3^2 * 5

Since 1260 is the LCM of M & N and 7M=9N, M should be 2^2 * 3^2 * 5 and N should be 7 * 2^2 * 5.

So the GCF of M & N is 2^2 * 5

i.e 20 .

So Answer is A
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 12 Sep 2026
Posts: 11,292
Own Kudos:
46,143
 [6]
Given Kudos: 339
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,292
Kudos: 46,143
 [6]
If M and N are two positive integers such that 7 times M is Mon Sep 20, 2021 3:56 am
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
PyjamaScientist
If M and N are two positive integers such that 7 times M is 9 times N and 1260 is the least number that is a multiple of both M and N, then which among the following is the greatest number that can divide both M and N ?

(a) 20
(b) 30
(c) 40
(d) 50
(e) 60
Show more

PyjamaScientist, you are perfectly fine with your method.

If I were to do this, I would take the HCF as x.

Now 7M = 9N means M has all factors of N apart from 7, and an extra factor of 9. So M=9x
Also, 7M = 9N means N has all factors of M apart from 9, and an extra factor of 7. So M=7x

LCM(7x,9x) = 7*9*x=1260…………x=20


A
General Discussion
User avatar
TestPrepUnlimited
User avatar
Joined: 16 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,221
Own Kudos:
1,157
 [3]
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,221
Kudos: 1,157
 [3]
If M and N are two positive integers such that 7 times M is Sat Aug 28, 2021 6:37 am
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
PyjamaScientist
If M and N are two positive integers such that 7 times M is 9 times N and 1260 is the least number that is a multiple of both M and N, then which among the following is the greatest number that can divide both M and N ?

(a) 20
(b) 30
(c) 40
(d) 50
(e) 60
Show more

7M = 9N = 1260. Since we cannot simplify down 7M = 9N, it must be equal to 1260 as that is the least common multiple.

M = 1260/7 = (1400 - 140)/7 = 200 - 20 = 180
N = 1260/9 = (900 + 360)/9 = 140.

The GCF of 180 and 140 is 20.

Ans: A
User avatar
PyjamaScientist
User avatar
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Last visit: 14 Jul 2026
Posts: 1,123
Own Kudos:
1,396
 [3]
Given Kudos: 633
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Products:
My Reviews
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Posts: 1,123
Kudos: 1,396
 [3]
If M and N are two positive integers such that 7 times M is Mon Sep 20, 2021 12:30 am
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
chetan2u Would you like to share your 2 cents on this. Here, I mistook N as M and vice versa. It does not make any difference to the final answer though. So, kindly ignore that.
Also, since I have taken, 7N = 9M. I concluded that N will be a multiple of 9 (since 7 isn't) and similarly M will be a multiple of 7 (since 9 isn't) and then continued with calculating the max values for both through the LCM given 1260. This 1260 gives me maximum powers that prime factors of either of M or N can take. So, maximizing powers for max value of M and N, along with the nature of N (=9k) and M (=7K), made me come to this final solution. How would you have done it?
Attachments

GC Sol.jpeg
GC Sol.jpeg [ 172.5 KiB | Viewed 7826 times ]

User avatar
bv8562
User avatar
Joined: 01 Dec 2020
Last visit: 01 Oct 2025
Posts: 402
Own Kudos:
514
Given Kudos: 360
GMAT 1: 680 Q48 V35
GMAT 1: 680 Q48 V35
Posts: 402
Kudos: 514
If M and N are two positive integers such that 7 times M is Thu Jan 27, 2022 5:09 am
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u Could you please tell me if I have done it right?

7M = 9N
M/N = 9/7

Product of two integers = Product of their LCM & HCF

M = 9k
N = 7k
LCM = 1260
HCF = x

M * N = 1260 * HCF
9*7*k*k = 1260 * x
x = 9*7*k^2/1260

x = k^2/20 (A)
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 12 Sep 2026
Posts: 11,292
Own Kudos:
46,143
Given Kudos: 339
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,292
Kudos: 46,143
If M and N are two positive integers such that 7 times M is Thu Jan 27, 2022 8:21 am
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bv8562
chetan2u Could you please tell me if I have done it right?

7M = 9N
M/N = 9/7

Product of two integers = Product of their LCM & HCF

M = 9k
N = 7k
LCM = 1260
HCF = x

M * N = 1260 * HCF
9*7*k*k = 1260 * x
x = 9*7*k^2/1260

x = k^2/20 (A)
Show more

You are absolutely correct.
avatar
Him2323
avatar
Joined: 21 Jun 2024
Last visit: 24 Apr 2025
Posts: 3
Given Kudos: 33
Posts: 3
Kudos: 0
If M and N are two positive integers such that 7 times M is Mon Sep 09, 2024 4:24 am
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­7M = 9N ---> Derived LCM(7,9) = 63

Actual LCM(M,N) = 1260

HCF = Actual LCM/Derived LCM = 1260/63 = 20 (option A)

Kindly confirm if there is any fault in this approach. Thanks.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,226
Own Kudos:
1,158
Posts: 39,226
Kudos: 1,158
If M and N are two positive integers such that 7 times M is Sun Jan 04, 2026 4:46 am
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
113474 posts