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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
If x, y, and z are all positive integers, what is the least common mul  [#permalink]

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If x, y, and z are all positive integers, what is the least common multiple of x, y, and z?

(1) The least common multiple of x and y is 15.

(2) The least common multiple of x and z is 18.

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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1021
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If x, y, and z are all positive integers, what is the least common mul  [#permalink]

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From statement 1:

No info about Z.
Insufficient.

From Statement 2:

No info about Y.
Insufficient.

Combining Both:

LCM of X and Y is 15.
LCM of X and Z is 18.

LCM of X, Y and Z is 9*5*2 = 90.
Sufficient..

C is the answer.
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Intern  B
Joined: 27 Nov 2018
Posts: 36
GMAT 1: 510 Q33 V28 Re: If x, y, and z are all positive integers, what is the least common mul  [#permalink]

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Bunuel wrote:
If x, y, and z are all positive integers, what is the least common multiple of x, y, and z?

(1) The least common multiple of x and y is 15.

(2) The least common multiple of x and z is 18.

Bunuel

LCM of xy = 15 => numbers can be 1x15, 5x3,
LCM of xz = 18 => numbers can be 1x18, 9x2, 6x3

x is the common number, so the numbers be like 1, 15, 18. Can you please tell how to find the values of x, y ,z specifically ?
Director  D
Joined: 19 Oct 2018
Posts: 981
Location: India
Re: If x, y, and z are all positive integers, what is the least common mul  [#permalink]

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1
Statement 1
LCM of xy = 15, we don't know the value of z
insufficient

Statement 2
The least common multiple of x and z is 18, we don't know the value of z
insufficient

Combining statement 1 and 2
x can be either 1 or 3
1. x=1, y=15 and z=18, LCM = 90
2. x=3, y=5 and z=18, LCM=90
3. x=3, y=15 and z=18 LCM=90
Sufficient

pandajee wrote:
Bunuel wrote:
If x, y, and z are all positive integers, what is the least common multiple of x, y, and z?

(1) The least common multiple of x and y is 15.

(2) The least common multiple of x and z is 18.

Bunuel

LCM of xy = 15 => numbers can be 1x15, 5x3,
LCM of xz = 18 => numbers can be 1x18, 9x2, 6x3

x is the common number, so the numbers be like 1, 15, 18. Can you please tell how to find the values of x, y ,z specifically ?
Intern  B
Joined: 27 Nov 2018
Posts: 36
GMAT 1: 510 Q33 V28 Re: If x, y, and z are all positive integers, what is the least common mul  [#permalink]

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nick1816 wrote:
Statement 1
LCM of xy = 15, we don't know the value of z
insufficient

Statement 2
The least common multiple of x and z is 18, we don't know the value of z
insufficient

Combining statement 1 and 2
x can be either 1 or 3
1. x=1, y=15 and z=18, LCM = 90
2. x=3, y=5 and z=18, LCM=90
3. x=3, y=15 and z=18 LCM=90
Sufficient

pandajee wrote:
Bunuel wrote:
If x, y, and z are all positive integers, what is the least common multiple of x, y, and z?

(1) The least common multiple of x and y is 15.

(2) The least common multiple of x and z is 18.

Bunuel

LCM of xy = 15 => numbers can be 1x15, 5x3,
LCM of xz = 18 => numbers can be 1x18, 9x2, 6x3

x is the common number, so the numbers be like 1, 15, 18. Can you please tell how to find the values of x, y ,z specifically ?

Thanks.. For all value of x & y having LCM as 15, z=18 will always give LCM of x,y,z as 90.
So, we don't need to worry about xz being 1x18 or 9x2 or 6x3... right ?
Director  D
Joined: 19 Oct 2018
Posts: 981
Location: India
Re: If x, y, and z are all positive integers, what is the least common mul  [#permalink]

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Exactly!! BTW you can't consider 6*3 because their LCM is 6 not 18

Thanks.. For all value of x & y having LCM as 15, z=18 will always give LCM of x,y,z as 90.
So, we don't need to worry about xz being 1x18 or 9x2 or 6x3... right ?[/quote]
Intern  B
Affiliations: National Institute of Technology, Durgapur
Joined: 22 Feb 2017
Posts: 38
Location: India
GPA: 3.6
WE: Engineering (Manufacturing)
If x, y, and z are all positive integers, what is the least common mul  [#permalink]

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Bunuel wrote:
If x, y, and z are all positive integers, what is the least common multiple of x, y, and z?

(1) The least common multiple of x and y is 15.

(2) The least common multiple of x and z is 18.

Hi, Bunuel

I want to clear my concept on LCM; Suppose LCM of any set 'n' & set 'm' are given and if we are asked to find LCM of all the no.s of set n & m combined it will simply be LCM [LCM (set n), LCM (set m)] why? as LCM is the least such no. which is divisible by all the no.s of set n & m.

If i'm wrong please clear my doubt!!
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-Chef Gordon Ramsey If x, y, and z are all positive integers, what is the least common mul   [#permalink] 23 Jul 2019, 11:57
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