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# Which of the following is the lowest positive integer that is divisibl

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Math Expert
Joined: 02 Sep 2009
Posts: 50770
Which of the following is the lowest positive integer that is divisibl  [#permalink]

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29 Mar 2016, 02:11
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Difficulty:

35% (medium)

Question Stats:

74% (01:34) correct 26% (02:01) wrong based on 100 sessions

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Which of the following is the lowest positive integer that is divisible by 8, 9, 10, 11, and 12?

A. 7,920
B. 5,940
C. 3,960
D. 2,970
E. 890

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Re: Which of the following is the lowest positive integer that is divisibl  [#permalink]

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29 Mar 2016, 03:44

890 - Not divisible by 12 (3 * 4) as the number is not divisible by 3.
2970 - Not divisible by 8 as the last three digits are not divisible by 8
3960 - Divisible by 3, 4, 8, 9, 10 and 11.

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Re: Which of the following is the lowest positive integer that is divisibl  [#permalink]

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29 Mar 2016, 03:59
Bunuel wrote:
Which of the following is the lowest positive integer that is divisible by 8, 9, 10, 11, and 12?

A. 7,920
B. 5,940
C. 3,960
D. 2,970
E. 890

No.'s are quite interesting in this case
like 2*2970 = 5940 and 2*3960=7920, this is something one should reveal himself at first look

Now looking at divisible no 8,9,10,11,12.. I will in a second try for 10, yups all no. are divisible by 10

Now for next contender i will look for a prime 11, kindly note even after dividing by 11 the no. should be divisible by 8,9,5 (out of minimum of 8, 9, 5 (10 as 2 is already considered with 8), 12 ( 4 and 3 already taken care with 8 and 9)

Starting with lowest = 890 / 11= 80 not divisible by 3
2970/11=270 not divisible by 8
3960/11= 360 divisible by 8,9,5 got it !!
7920/11 = 720 already checked 3960 so it will by having, but smaller one already filtered
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Re: Which of the following is the lowest positive integer that is divisibl  [#permalink]

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29 Mar 2016, 18:18
1
The question basically asks for the LCM of these numbers.

$$8 = 2 * 2 * 2$$

$$9 = 3 * 3$$

$$10 = 2 * 5$$

$$11 = 11$$

$$12 = 2 * 2 *3$$

LCM = $$2 * 2 * 2 *3 *3 * 5 * 11 = 3960$$
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Re: Which of the following is the lowest positive integer that is divisibl  [#permalink]

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30 Mar 2016, 03:12
LCM = lowest positive integer that is divisble means the LCM of these numbers 8,9,10,11,12 = 3960

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Re: Which of the following is the lowest positive integer that is divisibl  [#permalink]

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09 Sep 2018, 01:16
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Which of the following is the lowest positive integer that is divisibl &nbs [#permalink] 09 Sep 2018, 01:16
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