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# What is the lowest positive integer that is divisible by each of the

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Joined: 21 Oct 2013
Posts: 411
What is the lowest positive integer that is divisible by each of the  [#permalink]

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11 Oct 2014, 13:04
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35% (medium)

Question Stats:

70% (01:28) correct 30% (01:41) wrong based on 157 sessions

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What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?
A) 3×17×19×21
B) 5×17×19×23
C) 7×15×17×19
D) 7×15×19×21
E) 15×17×19×21
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Posts: 58317
Re: What is the lowest positive integer that is divisible by each of the  [#permalink]

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11 Oct 2014, 13:40
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goodyear2013 wrote:
What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?
A) 3×17×19×21
B) 5×17×19×23
C) 7×15×17×19
D) 7×15×19×21
E) 15×17×19×21

We should find the LCM of 15 = 3*5, 17, 19, and 21 = 3*7 --> LCM = 3*5*7*17*19 = 7*15*17*19.

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Re: What is the lowest positive integer that is divisible by each of the  [#permalink]

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16 Oct 2014, 00:15
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goodyear2013 wrote:
What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?
A) 3×17×19×21
B) 5×17×19×23
C) 7×15×17×19
D) 7×15×19×21
E) 15×17×19×21

We are looking for divisibility by 15, 17, 19, 21

17 & 19 are prime numbers >> They have to be in the integer required, so option D is ignored

LCM of 15 & 21 = 3 * 5 * 7 = $$15 * 7$$ OR $$35 * 3$$ OR 21 * 5

Option A, B & D can be ignored

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Re: What is the lowest positive integer that is divisible by each of the  [#permalink]

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21 Sep 2016, 06:42
goodyear2013 wrote:
What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?
A) 3×17×19×21
B) 5×17×19×23
C) 7×15×17×19
D) 7×15×19×21
E) 15×17×19×21

ok so we need to make sure that the number is divisible by 15, 17, 19, and 21.
it is mandatory to have 17 and 19.
15 = 3x5
21 = 3x7
so we need at least one factor of 3, then one of 5, and one of 7.

overall:
we need
1 factor of 3, 1 factor of 5, 1 factor of 7, 17, and 19.

C fits.
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Re: What is the lowest positive integer that is divisible by each of the  [#permalink]

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16 Feb 2019, 20:34
goodyear2013 wrote:
What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?
A) 3×17×19×21
B) 5×17×19×23
C) 7×15×17×19
D) 7×15×19×21
E) 15×17×19×21

Now odd integers will be 15,17,19,21

Highest value will be E

and lowest value will be C

since we are asked the lowest possible integer value, it is

C
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Re: What is the lowest positive integer that is divisible by each of the   [#permalink] 16 Feb 2019, 20:34
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