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# If x is the smallest positive integer that is divisible by each of the

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If x is the smallest positive integer that is divisible by each of the  [#permalink]

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Updated on: 29 Jan 2017, 06:34
1
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Difficulty:

55% (hard)

Question Stats:

67% (02:18) correct 33% (02:09) wrong based on 106 sessions

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If $$x$$ is the smallest positive integer that is divisible by each of the integers from $$24$$ to $$27$$ inclusive, which of the following statements must be true?

I) $$x > 3200$$
II) $$x$$ is a multiple of $$90$$
III) $$500$$ is a factor of $$x$$

A) I only
B) II only
C) I and II
D) II and III
E) I,II,III

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Originally posted by hazelnut on 28 Jan 2017, 17:36.
Last edited by hazelnut on 29 Jan 2017, 06:34, edited 1 time in total.
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Re: If x is the smallest positive integer that is divisible by each of the  [#permalink]

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28 Jan 2017, 20:48
x = 24 * 25 * 26 * 27
x = $$(2^2 * 3^2 * 5)^2 * 13$$

I) x>3200 - Yes

II) x is a multiple of 90. - Yes

III)500 is a factor of x. - No

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Re: If x is the smallest positive integer that is divisible by each of the  [#permalink]

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28 Jan 2017, 23:19
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ziyuenlau wrote:
If x is the smallest positive integer that is divisible by each of the integers from 24 to 27 inclusive,which of the following statements must be true?

I)x>3200
II)x is a multiple of 90.
III)500 is a factor of x.

A)I only
B)II only
C)I and II.
D)II and III
E)I,II,III

x = LCM of 24,25,26 & 27 = 70200

I)x>3200 - True
II)x is a multiple of 90. - True

III)500 is a factor of x. - False

Thus, only (C) I and II follows....
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Re: If x is the smallest positive integer that is divisible by each of the  [#permalink]

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11 Apr 2019, 18:33
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Re: If x is the smallest positive integer that is divisible by each of the   [#permalink] 11 Apr 2019, 18:33
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