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Manager  P
Joined: 13 Jun 2012
Posts: 203
Location: United States
WE: Supply Chain Management (Computer Hardware)
If the least common multiple of the first 800 positive integers is n,  [#permalink]

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4 00:00

Difficulty:   65% (hard)

Question Stats: 51% (01:27) correct 49% (01:30) wrong based on 94 sessions

### HideShow timer Statistics 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
CEO  V
Joined: 12 Sep 2015
Posts: 3848
Re: If the least common multiple of the first 800 positive integers is n,  [#permalink]

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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.

Cheers,
Brent
_________________
Manager  B
Joined: 04 Oct 2017
Posts: 81
Re: If the least common multiple of the first 800 positive integers is n,  [#permalink]

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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.

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.
CEO  V
Joined: 12 Sep 2015
Posts: 3848
Re: If the least common multiple of the first 800 positive integers is n,  [#permalink]

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2
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.

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