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Senior Manager  Joined: 30 Nov 2008
Posts: 421
Schools: Fuqua
If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 61% (01:38) correct 39% (01:42) wrong based on 590 sessions

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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.
CEO  B
Joined: 17 Nov 2007
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GMAT 1: 750 Q50 V40 Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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9
9
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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Senior Manager  Joined: 30 Nov 2008
Posts: 421
Schools: Fuqua
Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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6
15
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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SVP  Joined: 29 Aug 2007
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Re: If x is a positive 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. 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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Senior Manager  Joined: 30 Nov 2008
Posts: 421
Schools: Fuqua
Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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GMAT TIGER

Hum......Do you want to give another try? Senior Manager  Joined: 25 Oct 2006
Posts: 465
Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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Thanks to mrsmarthi and walker.....
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Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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2
2
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 .

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Manager  Joined: 07 Apr 2014
Posts: 101
Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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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..
Intern  Joined: 12 Dec 2015
Posts: 16
Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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1
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

Director  G
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Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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7
1
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: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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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
Senior Manager  G
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Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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2
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 multiple of x, 6  [#permalink]

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2
1
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.

We are given that x is a positive integer and need to determine the LCM of x, 6, and 9. If we can determine the value of x, then we can determine the LCM of x, 6, and 9.

Statement One Alone:

The least common multiple of x and 6 is 30.

Using the information in statement one, we see that x can be 5 since LCM(5, 6) = 30. However, x can be also 10, 15, or 30; any of these values of x would also make LCM(x, 6) = 30. This may seem insufficient to answer the question, but let’s determine the LCM of x, 6 and 9 using these values:

If x = 5, LCM(5, 6, 9) = 90.

If x = 10, LCM(10, 6, 9) = 90.

If x = 15, LCM(15, 6, 9) = 90.

If x = 30, LCM(30, 6, 9) = 90.

Since the LCM of x, 6, and 9 is always 90 for all possible values of x, we see that statement one is sufficient to answer the question.

Statement Two Alone:

The least common multiple of x and 9 is 45.

Using the information in statement two, we see that x can be 5 since LCM(5, 9) = 45. However, x can be also 15 or 45; any of these values of x would also make LCM(x, 9) = 45. This may seem insufficient to answer the question, but let’s determine the LCM of x, 6 and 9 using these values:

If x = 5, LCM(5, 6, 9) = 90.

If x = 15, LCM(15, 6, 9) = 90.

If x = 45, LCM(45, 6, 9) = 90.

Since the LCM of x, 6, and 9 is always 90 for all possible values of x, statement two alone is sufficient to answer the question.

Note: Using either statement, we’ve not determined a unique value for x. However, regardless what the value x is, we’ve determined a unique value for the LCM of x, 6 and 9.

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Re: If x is a positive integer, what is the least common multiple of x, 6  [#permalink]

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Just use basic concept

A. LCM(x,6,9) = LCM(30,9)=90
B. LCM(x,6,9) = LCM(45,6)=90

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