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If x is a positive integer, what is the least common

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If x is a positive integer, what is the least common [#permalink]

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If x is a positive integer, what is the least common multiple of x, 6 and 9?

(1) The least common multiple of x and 6 is 30.
(2) The least common multiple of x and 9 is 45.
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Re: DS - Number Properties [#permalink]

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GMAT TIGER wrote:
1) The least common multiple of x and 6 is 30: x could be 5, 10, 15 or 30. nsf.

LCM(5,6,9)=90; LCM(10,6,9)=90; LCM(15,6,9)=90; LCM(30,6,9)=90;
Sufficient
GMAT TIGER wrote:
2) The least common mutiple of x and 9 is 45: x is 5, 15, or 45. nsf.

the same. Sufficient

Hey, guys, is it rule? LCM(a,b,c)=LCM(LCM(a,b),c) ?

If yes, we can use it:
1) LCM(x,6,9) = LCM(30,9)=90
2) LCM(x,6,9) = LCM(45,6)=90

D
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Re: DS - Number Properties [#permalink]

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New post 10 Mar 2009, 11:11
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walker wrote:
GMAT TIGER wrote:
1) The least common multiple of x and 6 is 30: x could be 5, 10, 15 or 30. nsf.

LCM(5,6,9)=90; LCM(10,6,9)=90; LCM(15,6,9)=90; LCM(30,6,9)=90;
Sufficient
GMAT TIGER wrote:
2) The least common mutiple of x and 9 is 45: x is 5, 15, or 45. nsf.

the same. Sufficient

Hey, guys, is it rule? LCM(a,b,c)=LCM(LCM(a,b),c) ?

If yes, we can use it:
1) LCM(x,6,9) = LCM(30,9)=90
2) LCM(x,6,9) = LCM(45,6)=90

D


Exactly Walker, this is the short cut rule. LCM(a,b,c)=LCM(LCM(a,b),c).

From stmt1, it LCM of 2 numbers(x,6) is given as 30. So LCM 3 numbers is LCM(30,9). Sufficient.

From stmt2, again same explanation as stmt1.

Initially I tried to find what is x from stmt 1 and then find the LCM of 3 numbers. THis is time consuming when the ans can be picked in less than 30 sec. :)

I raised this question, since I wanted to know in how ways can people solve the question.

As GMAT TIGER did, trying to find the x value rather than finding the LCM.

No offense, just analysing where all there are possibilities that things can go wrong and that we should be cautious.

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Re: If x is a positive integer, what is the least common [#permalink]

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statement (1):
the least common multiple of x and (2)(3) is (2)(3)(5).
this means:
we KNOW x contains exactly one 5, because otherwise that 5 wouldn't be in the lcm.
x MAY contain a 2, a 3, both, or neither; any of these possibilities would yield the (2)(3) in the lcm. note that x cannot contain more than one 2 or 3, as those powers would then go into the lcm.
x cannot contain any other primes, because those primes would have to appear in the lcm, and they don't.
given these facts, you know that the lcm of x, (3)(2), and (3^2) is (2)(3^2)(5). if you don't see why right away, run through the possibilities.

--

statement (2):
use the same kind of analysis as that used for statement (1).
the lcm of x and (3^2) is (3^2)(5).
therefore,
we KNOW that x contains exactly one 5.
x MAY contain no, one, or two 3's.
x CANNOT contain any other primes.
same sort of reasoning used above --> the lcm must be (2)(3^2)(5); sufficient

Hence D.
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Re: DS - Number Properties [#permalink]

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mrsmarthi wrote:
If X is an integer, what is the Least Common Multiple of x, 6 and 9.

1) The least common multiple of x and 6 is 30
2) The least common mutiple of x and 9 is 45.

I know the question is simple, but wanted to see in how many ways can this be answered(ofcourse correctly).

DS is about logical solving. :) Lets get the ball rolling.


1. I guess I did it recently.

1) The least common multiple of x and 6 is 30: x could be 5, 10, 15 or 30. nsf.
2) The least common mutiple of x and 9 is 45: x is 5, 15, or 45. nsf.

togather x = 5 and 15 suffff....

C.
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Re: DS - Number Properties [#permalink]

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New post 09 Mar 2009, 22:31
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Hum......Do you want to give another try? :wink:

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Re: DS - Number Properties [#permalink]

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New post 10 Mar 2009, 05:22
mrsmarthi wrote:
GMAT TIGER

Hum......Do you want to give another try? :wink:

:shocked
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Re: DS - Number Properties [#permalink]

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New post 14 Mar 2009, 06:52
Thanks to mrsmarthi and walker.....
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Re: If X is an integer, what is the Least Common Multiple of x,6 [#permalink]

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mrsmarthi wrote:
If X is an integer, what is the Least Common Multiple of x,6 and 9.

1) The least common multiple of x and 6 is 30
2) The least common mutiple of x and 9 is 45.

I know the question is simple, but wanted to see in how many ways can this be answered(ofcourse correctly).

DS is about logical solving. :) Lets get the ball rolling.


1) the LCM of x and 6 is 30. That means you need to find the LCM of 30 and 9 --> sufficient

2) LCM of x and 9 is 45 . you need to find out the LCM of 45 and 9 . - > sufficient .

Answer D
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Re: If x is a positive integer, what is the least common [#permalink]

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Re: If x is a positive integer, what is the least common [#permalink]

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New post 06 Sep 2014, 05:10
mrsmarthi wrote:
If x is a positive integer, what is the least common multiple of x, 6 and 9?

(1) The least common multiple of x and 6 is 30.
(2) The least common multiple of x and 9 is 45.



from question : 6- 2*3
9- 3*3
x - prime factor of x

1. LCM(X,6) = 30

6-- 2,3 ; x can be 5 - 5 , 10 - 2*5 , 15 -3*5 , 30- 2*3*5... i.e x = 5 or 10 or 30 or 15 ... for all value of x -- LCM (x,6,9) - 90.


2. LCM(x, 9)=45 ;
9- 3, 3

x can be 5 or 15 or 45 .... for all value of x -- LCM (x,6,9) - 90.


hence D..

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Re: If x is a positive integer, what is the least common [#permalink]

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Re: If x is a positive integer, what is the least common [#permalink]

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First, find LCM of 9 and 6 = 18, and then find LCM of:

(I) 18 and 30 = 90, Suff
(II) 18 and 45= 90, Suff

Answer D

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If x is a positive integer, what is the least common [#permalink]

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New post 03 Sep 2017, 09:09
mrsmarthi wrote:
walker wrote:
GMAT TIGER wrote:
1) The least common multiple of x and 6 is 30: x could be 5, 10, 15 or 30. nsf.

LCM(5,6,9)=90; LCM(10,6,9)=90; LCM(15,6,9)=90; LCM(30,6,9)=90;
Sufficient
GMAT TIGER wrote:
2) The least common mutiple of x and 9 is 45: x is 5, 15, or 45. nsf.

the same. Sufficient

Hey, guys, is it rule? LCM(a,b,c)=LCM(LCM(a,b),c) ?

If yes, we can use it:
1) LCM(x,6,9) = LCM(30,9)=90
2) LCM(x,6,9) = LCM(45,6)=90

D


Exactly Walker, this is the short cut rule. LCM(a,b,c)=LCM(LCM(a,b),c).


Does anyone have an article I could go to in order to learn more about this? mrsmarthi, walker

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Re: If x is a positive integer, what is the least common [#permalink]

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New post 18 Sep 2017, 09:03
mrsmarthi wrote:
If x is a positive integer, what is the least common multiple of x, 6 and 9?

(1) The least common multiple of x and 6 is 30.
(2) The least common multiple of x and 9 is 45.


hi

LCM of x, 6, 9 is the same as the LCM of (x, 6) and 9..
statement 1 provides the LCM of (x, 6) sufficient ....

in the same line of reasoning, LCM of x, 6, 9 is the same as the LCM of ( x, 9) and 6...
statement 2 provides the LCM of (x, 9) sufficient...
D

cheers, if this helps ...

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Re: If x is a positive integer, what is the least common   [#permalink] 18 Sep 2017, 09:03
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