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# Which of the following is the lowest positive integer that

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Manager
Joined: 01 Nov 2007
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Which of the following is the lowest positive integer that [#permalink]  05 Feb 2008, 14:05
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50% (01:43) correct 50% (00:43) wrong based on 4 sessions
Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?
15,120
3,024
2,520
1,890
1,680
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
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Re: PS - Divisibility [#permalink]  05 Feb 2008, 14:07
JCLEONES wrote:
Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?
15,120
3,024
2,520
1,890
1,680

pull out the biggest numbers first
3^2
2^3
7
5

9*8*7*5 = 2,520
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Director
Joined: 01 May 2007
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Re: PS - Divisibility [#permalink]  05 Feb 2008, 14:26
Woah Woah woah...backup here. Biggest #s first. Can you elaborate on this problem. I believe this one came out of the OG 11.
Director
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Re: PS - Divisibility [#permalink]  05 Feb 2008, 18:54
What do we pull the biggest #s? Any why not "6"?
Director
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Re: PS - Divisibility [#permalink]  06 Feb 2008, 13:52
1
KUDOS
JCLEONES wrote:
Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?
15,120
3,024
2,520
1,890
1,680

ok so lets break our divisors down into prime factors, i.e $2,3,2^2,5,3*2,7, 2^3,3^2$

anything divisible by $3^2$, will be divisible by 3, anything divisible by $2^3$ will be divisible by $2, 2^2$
anything divisible by 2 and 3 will be divisible by 6. so by multiplying $5*7* 2^3*3^2 = 2520$ we will yield the LCD = 2520

now since 2520 is one of the options, bingo, this is the LOWEST POSITIVE INT ,i.e 1 ,as asked by the question
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Re: PS - Divisibility [#permalink]  06 Feb 2008, 14:43
Thanks like a dummy I didn't realize we were looking for the LCD!
Re: PS - Divisibility   [#permalink] 06 Feb 2008, 14:43
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