NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 01:13 It is currently 24 Apr 2024, 01:13
Decision Tracker
My Rewards
New posts
New comers' posts

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

If the least common multiple of integers x and y is 840,

SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
rxs0005
Senior Manager
Senior Manager
Joined: 07 Jun 2004
Posts: 438
Own Kudos [?]: 2829 [34]
Given Kudos: 22
Location: PA
Send PM
If the least common multiple of integers x and y is 840, [#permalink] New post   03 Dec 2010, 18:09
2
Kudos
32
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

64% (01:38) correct 36% (01:53) wrong based on 767 sessions
Hide Show timer Statistics
If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14815
Own Kudos [?]: 64888 [17]
Given Kudos: 426
Location: Pune, India
Send PM
Re: GCF LCM DS [#permalink] New post   04 Dec 2010, 07:08
12
Kudos
4
Bookmarks
Expert Reply
gettinit wrote:
VeritasPrepKarishma wrote:
rxs0005 wrote:
If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168


Remember a property of LCM and GCF:
If x and y are two positive integers, LCM * GCF = x* y
Stmnt 1: Just the GCF will give you the product of the two numbers. Not their individual values.
Stmnt 2: Knowing the value of y and LCM is not sufficient to get x.
x could be 840 or 105 or 5 etc.

Using both together, you get x = 840*56/168 = 280
Answer (C).


Karishma is this a known property? I have never ran across it before? I am not sure I understand why it works either. Can you please explain?


It is taught at school (though curriculums across the world vary)

Let us take an example to see why this works:

\(x = 60 = 2^2 * 3 * 5\)
\(y = 126 = 2*3^2*7\)

Now GCF here will be \(6 (= 2*3)\) (because that is all that is common to x and y)
LCM will be whatever is common taken once and the remaining i.e. \((2*3) * 2*5 * 3*7\)

When you multiply GCF with LCM, you get
\((2*3) * (2*3 *2*5 * 3*7)\) i.e. whatever is common comes twice and everything else that the two numbers had.

I can re-arrange this product to write it as \((2*3 * 2*5) * (2*3 * 3*7)\) i.e. 60*126

This is the product of the two numbers.
Since GCF has what is common to them and LCM has what is common to them written once and everything else, GCF and LCM will always multiply to give the two numbers.

Can you now think what will happen in case of 3 numbers?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14815
Own Kudos [?]: 64888 [9]
Given Kudos: 426
Location: Pune, India
Send PM
Re: GCF LCM DS [#permalink] New post   03 Dec 2010, 19:12
5
Kudos
4
Bookmarks
Expert Reply
rxs0005 wrote:
If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168


Remember a property of LCM and GCF:
If x and y are two positive integers, LCM * GCF = x* y
Stmnt 1: Just the GCF will give you the product of the two numbers. Not their individual values.
Stmnt 2: Knowing the value of y and LCM is not sufficient to get x.
x could be 840 or 105 or 5 etc.

Using both together, you get x = 840*56/168 = 280
Answer (C).
General Discussion
avatar
gettinit
Manager
Manager
Joined: 13 Jul 2010
Posts: 81
Own Kudos [?]: 218 [0]
Given Kudos: 7
Send PM
Re: GCF LCM DS [#permalink] New post   03 Dec 2010, 20:09
VeritasPrepKarishma wrote:
rxs0005 wrote:
If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168


Remember a property of LCM and GCF:
If x and y are two positive integers, LCM * GCF = x* y
Stmnt 1: Just the GCF will give you the product of the two numbers. Not their individual values.
Stmnt 2: Knowing the value of y and LCM is not sufficient to get x.
x could be 840 or 105 or 5 etc.

Using both together, you get x = 840*56/168 = 280
Answer (C).


Karishma is this a known property? I have never ran across it before? I am not sure I understand why it works either. Can you please explain?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92892
Own Kudos [?]: 618668 [3]
Given Kudos: 81574
Send PM
CAT Tests Forum Quiz Mode
Re: GCF LCM DS [#permalink] New post   04 Dec 2010, 07:17
1
Kudos
2
Bookmarks
Expert Reply
rxs0005 wrote:
If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168


The property Karishma used is often tested on GMAT. So, it's a must know property:
for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\).

See GMAT questions about this concept:
xy-a-multiple-of-102540.html?hilit=most%20important#p797667
data-sufficiency-problem-95872.html?hilit=most%20important#p737970

Hope it helps.
avatar
gettinit
Manager
Manager
Joined: 13 Jul 2010
Posts: 81
Own Kudos [?]: 218 [0]
Given Kudos: 7
Send PM
Re: GCF LCM DS [#permalink] New post   04 Dec 2010, 10:12
Thank you Karishma, makes sense. If I use three numbers I don't think this property will work based on the following example:

36 - 2^2*3^2
90 - 2*5*3^2
72- 2^3 * 3^2

GCF - 2*3^2 = 18
LCM - 2^3*3^2*5 = 360

so gcf*lcm=360*18=6480 which does not equal 36*90*72.

Bunuel thanks for the examples, helpful in reinforcing.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14815
Own Kudos [?]: 64888 [0]
Given Kudos: 426
Location: Pune, India
Send PM
Re: GCF LCM DS [#permalink] New post   04 Dec 2010, 14:03
Expert Reply
gettinit wrote:
Thank you Karishma, makes sense. If I use three numbers I don't think this property will work based on the following example:

36 - 2^2*3^2
90 - 2*5*3^2
72- 2^3 * 3^2

GCF - 2*3^2 = 18
LCM - 2^3*3^2*5 = 360

so gcf*lcm=360*18=6480 which does not equal 36*90*72.

Bunuel thanks for the examples, helpful in reinforcing.


Yes, that's right. It works only for two numbers.
avatar
shan123
Intern
Intern
Joined: 23 Nov 2010
Posts: 4
Own Kudos [?]: 75 [0]
Given Kudos: 14
Location: India
Send PM
Re: GCF LCM DS [#permalink] New post   18 Dec 2010, 20:44
Karishma,

Thanks for the detailed explanation.

Shanif.
Ur imagination is ur only limit
avatar
manwiththeharmonica
Intern
Intern
Joined: 13 May 2012
Posts: 24
Own Kudos [?]: 26 [0]
Given Kudos: 2
Schools: LBS '16 (A)
GMAT 1: 760 Q50 V41
Send PM
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   27 Sep 2012, 18:41
The question does not say the integers are positive. Is it implied? Factors are always positive so are GCDs and LCMs, but x could be a positive or a negative integer?

Posted from my mobile device
avatar
manwiththeharmonica
Intern
Intern
Joined: 13 May 2012
Posts: 24
Own Kudos [?]: 26 [0]
Given Kudos: 2
Schools: LBS '16 (A)
GMAT 1: 760 Q50 V41
Send PM
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   27 Sep 2012, 18:43
In that case the answer is E

Posted from my mobile device
User avatar
AccipiterQ
Manager
Manager
Joined: 26 Sep 2013
Posts: 151
Own Kudos [?]: 598 [0]
Given Kudos: 40
Concentration: Finance, Economics
Schools: HBS '16 (D) Sloan '16 (D) Carroll '16 (WA$) Boston U '16 (A$) Northeastern '16 (A)
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Send PM
Re: GCF LCM DS [#permalink] New post   15 Oct 2013, 17:50
VeritasPrepKarishma wrote:

Let us take an example to see why this works:

\(x = 60 = 2^2 * 3 * 5\)
\(y = 126 = 2*3^2*7\)

Now GCF here will be \(6 (= 2*3)\) (because that is all that is common to x and y)
LCM will be whatever is common taken once and the remaining i.e. \((2*3) * 2*5 * 3*7\)

When you multiply GCF with LCM, you get
\((2*3) * (2*3 *2*5 * 3*7)\) i.e. whatever is common comes twice and everything else that the two numbers had.

I can re-arrange this product to write it as \((2*3 * 2*5) * (2*3 * 3*7)\) i.e. 60*126

This is the product of the two numbers.
Since GCF has what is common to them and LCM has what is common to them written once and everything else, GCF and LCM will always multiply to give the two numbers.

Can you now think what will happen in case of 3 numbers?


You've got to be kidding me....that makes perfect sense. I'm glad I'm taking the GMAT, I'm learning all these fascinating formulas I've never used before.
User avatar
AccipiterQ
Manager
Manager
Joined: 26 Sep 2013
Posts: 151
Own Kudos [?]: 598 [0]
Given Kudos: 40
Concentration: Finance, Economics
Schools: HBS '16 (D) Sloan '16 (D) Carroll '16 (WA$) Boston U '16 (A$) Northeastern '16 (A)
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Send PM
Re: GCF LCM DS [#permalink] New post   15 Oct 2013, 18:01
Bunuel wrote:
rxs0005 wrote:
If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168


The property Karishma used is often tested on GMAT. So, it's a must know property:
for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\).

See GMAT questions about this concept:
xy-a-multiple-of-102540.html?hilit=most%20important#p797667
data-sufficiency-problem-95872.html?hilit=most%20important#p737970

Hope it helps.



Is there a sheet with the 'must-know' type stuff on it? I know there's the PDF you guys put together, but is there anything that is just a one or two page listing of the commonly used formulas like this?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14815
Own Kudos [?]: 64888 [0]
Given Kudos: 426
Location: Pune, India
Send PM
Re: GCF LCM DS [#permalink] New post   15 Oct 2013, 21:32
Expert Reply
AccipiterQ wrote:
Is there a sheet with the 'must-know' type stuff on it? I know there's the PDF you guys put together, but is there anything that is just a one or two page listing of the commonly used formulas like this?


The list of must-know formulas would be really short and you would know most of the formulas on it (e.g. Distance = Speed*Time, Sum of first n positive integers = n(n+1)/2, area of a circle = pi*r^2 etc). Even if there are a couple that you don't know, you will come across them while preparing so just jot them down.

There will be many more formulas that you could find useful in particular questions but you can very easily manage without them. Also, learning too many formulas creates confusion about their usage - when to use which one - and hence they should be avoided.
User avatar
ronr34
Senior Manager
Senior Manager
Joined: 08 Apr 2012
Posts: 259
Own Kudos [?]: 239 [0]
Given Kudos: 58
Send PM
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   18 Jun 2014, 23:39
VeritasPrepKarishma wrote:
rxs0005 wrote:
If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168


Remember a property of LCM and GCF:
If x and y are two positive integers, LCM * GCF = x* y
Stmnt 1: Just the GCF will give you the product of the two numbers. Not their individual values.
Stmnt 2: Knowing the value of y and LCM is not sufficient to get x.
x could be 840 or 105 or 5 etc.

Using both together, you get x = 840*56/168 = 280
Answer (C).


Hi Karishma,

Stmnt 2: if we know the value of y, and the least common multiple, i can't think of another number that X could be other than 5.
Can you give an example?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14815
Own Kudos [?]: 64888 [0]
Given Kudos: 426
Location: Pune, India
Send PM
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   18 Jun 2014, 23:50
Expert Reply
ronr34 wrote:

Hi Karishma,

Stmnt 2: if we know the value of y, and the least common multiple, i can't think of another number that X could be other than 5.
Can you give an example?


I have given some values that x can take from statement 2 - "x could be 840 or 105 or 5 etc"
Note that we don't know the value of GCF from stmnt 2 alone. Hence, x could take many different values. Only when we know the GCF too, can we find the value of x.
avatar
raj4ueclerx
Intern
Intern
Joined: 13 May 2015
Posts: 3
Own Kudos [?]: 5 [0]
Given Kudos: 14
Location: India
GMAT Date: 09-12-2015
Send PM
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   18 Jun 2015, 22:41
VeritasPrepKarishma wrote:
ronr34 wrote:

Hi Karishma,

Stmnt 2: if we know the value of y, and the least common multiple, i can't think of another number that X could be other than 5.
Can you give an example?


I have given some values that x can take from statement 2 - "x could be 840 or 105 or 5 etc"
Note that we don't know the value of GCF from stmnt 2 alone. Hence, x could take many different values. Only when we know the GCF too, can we find the value of x.



Hi Karishma:

Can you please help me understand how can one find other numbers of x whose LCM will 840?
User avatar
Harley1980
Retired Moderator
Joined: 06 Jul 2014
Posts: 1010
Own Kudos [?]: 6339 [0]
Given Kudos: 178
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Send PM
GMAT ToolKit User
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   18 Jun 2015, 23:52
raj4ueclerx wrote:
VeritasPrepKarishma wrote:
ronr34 wrote:

Hi Karishma,

Stmnt 2: if we know the value of y, and the least common multiple, i can't think of another number that X could be other than 5.
Can you give an example?


I have given some values that x can take from statement 2 - "x could be 840 or 105 or 5 etc"
Note that we don't know the value of GCF from stmnt 2 alone. Hence, x could take many different values. Only when we know the GCF too, can we find the value of x.



Hi Karishma:

Can you please help me understand how can one find other numbers of x whose LCM will 840?


Hello raj4ueclerx.
Here is nice thread exclusively about finding LCM and GCF
having-issues-with-finding-lcm-and-gcf-can-someone-help-146965.html
avatar
raj4ueclerx
Intern
Intern
Joined: 13 May 2015
Posts: 3
Own Kudos [?]: 5 [0]
Given Kudos: 14
Location: India
GMAT Date: 09-12-2015
Send PM
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   19 Jun 2015, 01:13
Thanks for the suggestion....but I am still unable to find...How to come up with various values of X given that LCM(x, Y=168) = 840. Can some one please help me or show me the reverse calculation to derive x?
User avatar
Harley1980
Retired Moderator
Joined: 06 Jul 2014
Posts: 1010
Own Kudos [?]: 6339 [2]
Given Kudos: 178
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Send PM
GMAT ToolKit User
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   19 Jun 2015, 03:42
2
Kudos
raj4ueclerx wrote:
Thanks for the suggestion....but I am still unable to find...How to come up with various values of X given that LCM(x, Y=168) = 840. Can some one please help me or show me the reverse calculation to derive x?


Hello raj4ueclerx

at first you should find all primes in both numbers
168 = 2*2*2*3*7
840 = 2*2*2*3*5*7

So we see that 840 has 5 as prime and 168 not. This number is only difference between 168 and 840
so any number that equal to product of this numbers 2, 2, 2, 3, 5, 7 (any combination that include 5) will give as LCM = 840 with number 168
for example
2*5 = 10 LCM (10, 168) = 840
3*5 = 15 LCM (15, 168) = 840
2*2*2*5 = 40 LCM (40, 168) = 840
and so on

Does that makes sense?
avatar
raj4ueclerx
Intern
Intern
Joined: 13 May 2015
Posts: 3
Own Kudos [?]: 5 [0]
Given Kudos: 14
Location: India
GMAT Date: 09-12-2015
Send PM
Re: If the least common multiple of integers x and y is 840, [#permalink] New post   19 Jun 2015, 04:45
at first you should find all primes in both numbers
168 = 2*2*2*3*7
840 = 2*2*2*3*5*7

So we see that 840 has 5 as prime and 168 not. This number is only difference between 168 and 840
so any number that equal to product of this numbers 2, 2, 2, 3, 5, 7 (any combination that include 5) will give as LCM = 840 with number 168
for example
2*5 = 10 LCM (10, 168) = 840
3*5 = 15 LCM (15, 168) = 840
2*2*2*5 = 40 LCM (40, 168) = 840
and so on

Does that makes sense?[/quote]


Million thanks ...this helps :)
GMAT Club Bot
gmatclubot
Re: If the least common multiple of integers x and y is 840, [#permalink]
19 Jun 2015, 04:45
 1   2   
Moderator:
Bunuel
Math Expert
92888 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions