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12 Nov 2019, 02:50
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (02:42) correct
47%
(02:48)
wrong
based on 408
sessions
History
Date
Time
Result
Not Attempted Yet
If the highest common factor of 2,472, 1,284 and positive integer N is 12 and the least common multiple of the same three numbers, 2472, 1284 and N, is \(2^3*3^2*5*103*107\), what is the value of N?
(A) \(2^2 * 3^2 * 7\)
(B) \(2^2 * 3^3 * 103\)
(C) \(2^2 * 3^2 * 5\)
(D) \(2^2 * 3 * 5\)
(E) None of these
Are You Up For the Challenge: 700 Level Questions
(A) \(2^2 * 3^2 * 7\)
(B) \(2^2 * 3^3 * 103\)
(C) \(2^2 * 3^2 * 5\)
(D) \(2^2 * 3 * 5\)
(E) None of these
Are You Up For the Challenge: 700 Level Questions
12 Nov 2019, 07:38
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Bunuel
If the highest common factor of 2,472, 1,284 and positive integer N is 12 and the least common multiple of the same three numbers, 2472, 1284 and N, is \(2^3*3^2*5*103*107\), what is the value of N?
(A) \(2^2 * 3^2 * 7\)
(B) \(2^2 * 3^3 * 103\)
(C) \(2^2 * 3^2 * 5\)
(D) \(2^2 * 3 * 5\)
(E) None of these
Are You Up For the Challenge: 700 Level Questions
(A) \(2^2 * 3^2 * 7\)
(B) \(2^2 * 3^3 * 103\)
(C) \(2^2 * 3^2 * 5\)
(D) \(2^2 * 3 * 5\)
(E) None of these
Are You Up For the Challenge: 700 Level Questions
\(2472=2*2*2*3*103=2^3*3*103\).
\(1284=2*2*3*107=2^2*3*107\).
LCM=\(2^3*3^2*5*103*107\)
we can check each prime number
2 -- there can be two or 3 2s...\(2^2\) or \(2^3\)
3 -- Surely two 3s as LCM has two 3s but none of 1284 or 2472 have two 3s...\(3^2\)
5 -- Surely one 5..\(5^1\)
103 -- can be none or one of 103...\(103^0\) or \(103^1\)
107 -- can be none or one of 107...\(107^0\) or \(107^1\)
As there are two 3s, A, B and D are out...
N can be any of -
\(2^2*3^2*5\) and any of the combination of 2, 103 or 107 added to it..
for example \(2^3*3^2*5*103*107\) can be the largest value
C
Note : The question should ask for the smallest value of N or it should be ' What can be the value of N?'
13 Nov 2019, 04:21
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Solution
Given
- • HCF of 2,472, 1,284 and positive integer N is 12.
• LCM of 2,472, 1,284 and positive integer N is 2^3∗3^2∗5∗103∗107.
To find
- • The value of N.
Approach and Working out
- • 2472 = 2^3 * 3 * 103
• 1284 = 2^2 * 3 * 107
• HCF (2472, 1284, N) = 12
- o So, N = 2^(2+b) * 3^a * other prime factors where a >= 1 and b>=0
• LCM (2472, 1284, N) = 2^3∗3^2∗5∗103∗107.
- o So, N can be 2^(2+b) * 3^2 * 5 * 103^c * 107^d where:
- b, c, d can be 0 or 1
Only possible option is option C.
Thus, option C is the correct answer.
Correct Answer: Option C
