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If the least common multiple of the first 800 positive integers is n,
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22 Aug 2022, 01:44
22 Aug 2022, 01:44
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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
a. n
b. 9n
c. 89n
d. 800n
e. 801n
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If the least common multiple of the first 800 positive integers is n,
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22 Aug 2022, 07:26
22 Aug 2022, 07:26
1
Carcass 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
a. n
b. 9n
c. 89n
d. 800n
e. 801n
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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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If the least common multiple of the first 800 positive integers is n,
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27 Oct 2022, 10:25
27 Oct 2022, 10:25
Given that LCM of the first 800 positive integers is n and we need to find what is the least common multiple of the first 801 positive integers in terms of n
801 = 9 * 89
and both 9 and 89 are already present in the numbers from 1 to 800
=> LCM(First 800 numbers) = LCM(First 801 numbers) = n
Example: LCM of First 5 positive integers (1, 2, 3, 4, 5) = 3 * 4 * 5 = 60
LCM of First 6 positive integers (1, 2, 3, 4, 5, 6) is also 60 as 6 = 2*3 and both 2 and 3 are already considered in numbers from 1 to 5
So, Answer will be A
Hope it helps!
To learn more about LCM and GCD watch the following videos
801 = 9 * 89
and both 9 and 89 are already present in the numbers from 1 to 800
=> LCM(First 800 numbers) = LCM(First 801 numbers) = n
Example: LCM of First 5 positive integers (1, 2, 3, 4, 5) = 3 * 4 * 5 = 60
LCM of First 6 positive integers (1, 2, 3, 4, 5, 6) is also 60 as 6 = 2*3 and both 2 and 3 are already considered in numbers from 1 to 5
So, Answer will be A
Hope it helps!
To learn more about LCM and GCD watch the following videos
