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

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Math Expert
Joined: 02 Sep 2009
Posts: 58436
If n and x are positive integers, what is the least common multiple of  [#permalink]

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28 Apr 2016, 03:33
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Difficulty:

55% (hard)

Question Stats:

66% (01:59) correct 34% (02:04) wrong based on 163 sessions

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If n and x are positive integers, what is the least common multiple of 192 and 45n?

(1) n = 2^x
(2) n is a prime.

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Joined: 01 Jul 2010
Posts: 58
Location: India
GMAT 1: 660 Q43 V38
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Re: If n and x are positive integers, what is the least common multiple of  [#permalink]

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28 Apr 2016, 04:39
1
From the question stem we can infer
192 = 2^6*3
45n = 3^2*5*n

Stmnt 1
n=2^x
Depending upon the value of x the LCM (192,45n) can have different answers
Insufficient

Stmnt 2
n is prime so n can be 2,3,5,7 etc
Depending on the value of n LCM(192,45n) can have different answers
InSufficient

Stmnt 1 +2
This means that n can have only one value 2
So LCM (192,90) will be one single value
Sufficient

Ans C
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Joined: 06 Jul 2016
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Re: If n and x are positive integers, what is the least common multiple of  [#permalink]

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20 Jul 2017, 12:46
Bunuel wrote:
If n and x are positive integers, what is the least common multiple of 192 and 45n?

(1) n = 2^x
(2) n is a prime.

We need to find the value of n.

1) n = $$2^x$$
n = 2, 4, 8,.... etc.
Insufficient.

2) n is prime
n = 2,3,5,7,... etc.
Insufficient.

1+2)
n = $$2^x$$ and n is prime
=> x = 1 and n = 2
LCM (192,90) = Some unique number.
Sufficient.

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

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30 Aug 2018, 06:29
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Re: If n and x are positive integers, what is the least common multiple of   [#permalink] 30 Aug 2018, 06:29
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