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# The positive integer y is a multiple of (25)(610) and 3014. Which of t

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Intern
Joined: 13 Aug 2017
Posts: 8
The positive integer y is a multiple of (25)(610) and 3014. Which of t  [#permalink]

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15 Sep 2018, 16:39
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Difficulty:

15% (low)

Question Stats:

90% (02:03) correct 10% (02:29) wrong based on 34 sessions

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Math Expert
Joined: 02 Aug 2009
Posts: 7684
Re: The positive integer y is a multiple of (25)(610) and 3014. Which of t  [#permalink]

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15 Sep 2018, 19:48
1
neiln413b wrote:
Hello everyone

(image attached)
Any ideas on how to approach this problem? I know it involves prime factorization, but I can't figure out how to best approach it.

$$2^5*6^{10}=2^5*2^{10}*3^{10}.........30^{14}=2^{14}*3^{14}*5^{14}$$
Common multiple ...LCM = 2^{15}*3^{14}*5^{14}

Now any of the choices that has power of 2, 3 and 5 more than 15, 14 and 14 respectively will NOT be an integer..
A) 12,8,10 respectively......OK
B) 15,10, and 12 respectively...ok
C) 14,12,10.....OK
D) 12,14,7......Ok
E) 10,16,8....power of 3 is more than 14...NO

E
_________________
Re: The positive integer y is a multiple of (25)(610) and 3014. Which of t   [#permalink] 15 Sep 2018, 19:48
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