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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, 14:18
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  45% (medium)

Question Stats:

55% (01:20) correct 45% (01:20) wrong based on 47 sessions

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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, 14:29
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

Cheers,
Brent
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Re: If the least common multiple of the first 800 positive integers is n, &nbs [#permalink] 04 Oct 2018, 14:29
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If the least common multiple of the first 800 positive integers is n,

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