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If the least common multiple of the first 800 positive integers is n,

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If the least common multiple of the first 800 positive integers is n,  [#permalink]

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New post 04 Oct 2018, 15:18
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If the least common multiple of the first 800 positive integers is n, then what is the least common multiple of the first 801 positive integers in terms of n ?


a. n
b. 9n
c. 89n
d. 800n
e. 801n
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Re: If the least common multiple of the first 800 positive integers is n,  [#permalink]

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New post 04 Oct 2018, 15:29
Top Contributor
Turkish wrote:
If the least common multiple of the first 800 positive integers is n, then what is the least common multiple of the first 801 positive integers in terms of n ?


a. n
b. 9n
c. 89n
d. 800n
e. 801n


The least common multiple of the first 800 positive integers is n
So, n is a multiple of 1, a multiple of 2, a multiple of 3, a multiple of 4, . . . a multiple of 9, . . . ., a multiple of 89, . . . a multiple of 799, and a multiple of 800

What is the least common multiple of the first 801 positive integers in terms of n ?
801 = (9)(89)
In other words, 801 is a multiple of 9, and 801 is a multiple of 89
Since n is already a multiple of 9 and a multiple of 89, we know that n must be a multiple of 801

So, if n is the least common multiple of the first 800 positive integers, n is also the least common multiple of the first 801 positive integers.

Answer: A

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Brent
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Re: If the least common multiple of the first 800 positive integers is n,  [#permalink]

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New post 11 Dec 2018, 06:34
GMATPrepNow wrote:
Turkish wrote:
If the least common multiple of the first 800 positive integers is n, then what is the least common multiple of the first 801 positive integers in terms of n ?


a. n
b. 9n
c. 89n
d. 800n
e. 801n


The least common multiple of the first 800 positive integers is n
So, n is a multiple of 1, a multiple of 2, a multiple of 3, a multiple of 4, . . . a multiple of 9, . . . ., a multiple of 89, . . . a multiple of 799, and a multiple of 800

What is the least common multiple of the first 801 positive integers in terms of n ?
801 = (9)(89)
In other words, 801 is a multiple of 9, and 801 is a multiple of 89
Since n is already a multiple of 9 and a multiple of 89, we know that n must be a multiple of 801

So, if n is the least common multiple of the first 800 positive integers, n is also the least common multiple of the first 801 positive integers.

Answer: A

Cheers,
Brent


Hi Brent,

I solved it as follows. Please correct me if I am wrong.

I assumed the numbers to be 1,2,3,4,5. LCM is 60
LCM of 1,2,3,4,5,6 is also 60.

Hence A.
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Re: If the least common multiple of the first 800 positive integers is n,  [#permalink]

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New post 11 Dec 2018, 08:33
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Top Contributor
Kezia9 wrote:
GMATPrepNow wrote:
Turkish wrote:
If the least common multiple of the first 800 positive integers is n, then what is the least common multiple of the first 801 positive integers in terms of n ?


a. n
b. 9n
c. 89n
d. 800n
e. 801n


The least common multiple of the first 800 positive integers is n
So, n is a multiple of 1, a multiple of 2, a multiple of 3, a multiple of 4, . . . a multiple of 9, . . . ., a multiple of 89, . . . a multiple of 799, and a multiple of 800

What is the least common multiple of the first 801 positive integers in terms of n ?
801 = (9)(89)
In other words, 801 is a multiple of 9, and 801 is a multiple of 89
Since n is already a multiple of 9 and a multiple of 89, we know that n must be a multiple of 801

So, if n is the least common multiple of the first 800 positive integers, n is also the least common multiple of the first 801 positive integers.

Answer: A

Cheers,
Brent


Hi Brent,

I solved it as follows. Please correct me if I am wrong.

I assumed the numbers to be 1,2,3,4,5. LCM is 60
LCM of 1,2,3,4,5,6 is also 60.

Hence A.


It's a useful strategy to examine a smaller case (first 5 positive integers vs the first 800 positive integers), but it happens to be a lucky coincidence that you found the correct answer.
For example, if you had examined the first 4 positive integers, you would have gotten a different answer.
If the numbers are 1, 2, 3, 4, then the LCM = 12
But the LCM of 1, 2, 3, 4, and 5 is not 12 (it's 60)

Cheers,
Brent
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Re: If the least common multiple of the first 800 positive integers is n,   [#permalink] 11 Dec 2018, 08:33
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