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Which of the following is the lowest positive integer that

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

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Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Jan 2013, 16:23, edited 1 time in total.
Renamed the topic and edited the question.

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

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sambam wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500


The first 7 positive multiples of 5 are 5, 10, 15, 20, 25, 30 and 35. The least common multiple of these numbers is 2,100.

Answer: D.

Or, a shortcut approach:
Discard 140, 1,400 and 3,500 because they are not divisible by 3.
Discard 210 because it's not divisible by 4.
Only option D remains.
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Re: Which of the following is the lowest positive integer that [#permalink]

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New post 10 Jan 2013, 18:53
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hitman5532 wrote:
Bunuel wrote:
sambam wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500


The first 7 positive multiples of 5 are 5, 10, 15, 20, 25, 30 and 35. The least common multiple of these numbers is 2,100.

Answer: D.

Or:
Discard 140, 1,400 and 3,500 because they are not divisible by 3.
Discard 210 because it's not divisible by 4.
Only option D remains.



Why are we looking at divisibility by 3 and 4?


The least common multiple of 5, 10, 15, 20, 25, 30 and 35 must be a multiple of 3 since 15 is a multiple of 3 and it must a multiple of 4 since 20 is a multiple of 4.

Hope it's clear.
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Re: Which of the following is the lowest positive integer that [#permalink]

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honchos wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?
140
210
1400
2100
3500


One way to look at it this :

1st 7 multiples of 5:
5 =1*5
10=2*5
15=3*5
20=4*5=2^2*5
25=5^2
30=2*3*5
35=5*7

Always try to break down the numbers into their corresponding prime factors.

For LCM (least common multiple) take the highest powers of 2,3,5,7 which gives us : 2^2 *3*5^2*7 = 2100. Hence D is the correct answer.

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

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New post 10 Jan 2013, 17:58
Bunuel wrote:
sambam wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500


The first 7 positive multiples of 5 are 5, 10, 15, 20, 25, 30 and 35. The least common multiple of these numbers is 2,100.

Answer: D.

Or:
Discard 140, 1,400 and 3,500 because they are not divisible by 3.
Discard 210 because it's not divisible by 4.
Only option D remains.



Why are we looking at divisibility by 3 and 4?

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

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New post 10 Jan 2013, 18:33
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500

Take 5,10,15,20,25,30, and 35

You can eliminate A and B right off the bat because 25 doesn't go into 140 or 210. I found it easier to look take a two of the multiples and test their divisibility among the choices. If one doesn't work its wrong so 30 and 35.

C) Wrong not divisible by 30
D) Yes for both check 15 that's the only other obscure multiple
E) Not divisible by 30

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

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New post 10 Jan 2013, 19:38
I knew I was missing something very simple. Thank you

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

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New post 10 Jan 2013, 20:25
first 7 positive multiples of 5 are 5, 10, 15, 20, 25, 30 and 35.

5 = 1* 5
10 = 2 * 5
15 = 3 * 5
20 = 4 * 5 = \(2^2 * 5\)
25 = 5 * 5 = \(5 ^ 5\)
30 = 6 * 5= \(2*3*5\)
35 = 7* 5

So, LCM would be 1 * \(2^2\) * 3 * \(5^5\) * 7 = 2100

actually i made mistake while computing first after going through Bunuel soln i got above one :-D
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Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?
140
210
1400
2100
3500
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New post 10 Jul 2015, 02:11
This is quite tough bunuel your input needed.
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Re: Which of the following is the lowest positive integer that [#permalink]

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New post 10 Jul 2015, 02:14
honchos wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?
140
210
1400
2100
3500


Merging topics.

Please search before posting and name topics properly. Also, please put A, B, C, D, and E in front of the options. Thank you.
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Re: Which of the following is the lowest positive integer that [#permalink]

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New post 29 May 2017, 15:58
sambam wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500


First write out in a single column the first seven positive multiples of 5:

5
10
15
20
25
30
35

Then in the next column write out their prime factors:

5
2*5
3*5
2^2*5
5^2
2*3*5
7*5

For an integer to be divisible by each of these prime groups, it must have all of these primes at their highest power. So it must have at least 5^2 for instance because 5^2 is 25 and this integer must be divisible by 25.

We can narrow the list down to 5^2*7*2^2*3

100*7*3

100*21 = 2100.

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Re: Which of the following is the lowest positive integer that   [#permalink] 29 May 2017, 15:58
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