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If x and n are positive integers, what is the least common multiple of

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If x and n are positive integers, what is the least common multiple of  [#permalink]

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New post 03 Nov 2018, 10:11
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If x and n are positive integers, what is the least common multiple of 96 and x?
1) x = \(2^n * 3^2 *5\)
2) n < 5

Weekly Quant Quiz #7 Question No 6


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Re: If x and n are positive integers, what is the least common multiple of  [#permalink]

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New post 03 Nov 2018, 10:30
Prime factor of 96 = \(2^5*3^1\)

From statement 1:

x = \(2^n3^25^1\)
LCM of 96 and x will be \(2^n3^25^1\).
LCM is dependent on n.
Hence insufficient.

From statement 2:

only n is given no info about x.
Insufficient.

Combining both
n<5.
Then LCM will be \(2^53^25^1\)

C is the answer.
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Re: If x and n are positive integers, what is the least common multiple of  [#permalink]

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New post 03 Nov 2018, 10:37
If x and n are positive integers, what is the least common multiple of 96 and x?
1) x = 2n∗32∗52n∗32∗5
2) n < 5


Lcm of 96 and x.
Prime factorisation of 96: 2^5*3^1

Now. Statement 1:
Lcm can be calculated by taking the highest prime facotrs of both the integers.
Now since the value of n is unknown there can be 2 cases:

N less than or equal tp 5: LCM= 5*9*2^5
N more than 5:: Lcm = 5*9*2^n

hence since 2 values, NS

Statement 2: clearly NS.

Combine : CLearly sufficient.

Hence, ANS C
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Re: If x and n are positive integers, what is the least common multiple of  [#permalink]

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New post 03 Nov 2018, 10:38
If x and n are positive integers, what is the least common multiple of 96 and x?

Option A: x= (2^n) * (3^2)*5

96= 2*2*2*2*2*3= (2^5)*3

LCM of 96 and x is not sure because if n < 5, it will be 2^5*3^2*5. and if n>5 it will be (2^n)*3^2*5

so option A is not sufficient

Option B: n< 5
wow this definitely leads to the answer

so B is sufficient
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Re: If x and n are positive integers, what is the least common multiple of  [#permalink]

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New post 03 Nov 2018, 10:48
e_) both are not sufficiet as 96=2power 5 x3
and for LCM we need to get n it can be 1,2,3,4 so we cant find the real lcm
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Re: If x and n are positive integers, what is the least common multiple of  [#permalink]

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New post 04 Nov 2018, 02:17
We need to find LCM of 96 and x or \(2^5 * 3 , x\)

Statement 1 :
\(x = 2^n * 3^2 * 5\)

LCM = \(2^n * 3^2* 5\)
or \(2^5* 3^2 * 5\)

Since we don't know whether n <= 5 , we cannot find the lcm

Statement 2 :
n < 5
It gives us nothing to go on

Together :
No we know n < 5 ; LCM = \(2^5* 3^2 * 5\)

Ans C
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Re: If x and n are positive integers, what is the least common multiple of   [#permalink] 04 Nov 2018, 02:17
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