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If the highest common factor of 2,472, 1,284 and positive integer N is
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12 Nov 2019, 02:50
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46% (02:30) correct 54% (02:26) wrong based on 78 sessions
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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
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Re: If the highest common factor of 2,472, 1,284 and positive integer N is
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12 Nov 2019, 07:38
Bunuel wrote: 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\(2472=2*2*2*3*103=2^3*3*103\). \(1284=2*2*3*107=2^2*3*107\). 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?'
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If the highest common factor of 2,472, 1,284 and positive integer N is
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13 Nov 2019, 04:21
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 findApproach 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:
Only possible option is option C. Thus, option C is the correct answer. Correct Answer: Option C
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Re: If the highest common factor of 2,472, 1,284 and positive integer N is
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15 Nov 2019, 08:01
EgmatQuantExpert wrote: 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 findApproach 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:
Only possible option is option C. Thus, option C is the correct answer. Correct Answer: Option CHow about this approach ? HCM X LCM = Product of numbers 2472 X 1284 X N = 12 X 2^3 X 3^2 X 5 X 103 X 107 solving it results in N = 3*5 = 15



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Re: If the highest common factor of 2,472, 1,284 and positive integer N is
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20 Nov 2019, 18:58
Bunuel wrote: 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 QuestionsLet’s first factor 2,472 and 1,284 into primes: 2,472 = 12 x 206 = 2^2 x 3 x 2 x 103 = 2^3 x 3 x 103 1,284 = 12 x 107 = 2^2 x 3 x 107 We see that that the LCM of 2,472 and 1,284 is 2^3 x 3 x 103 x 107. Notice that the LCM of 2,472 1,284, and N is equal to the LCM of 2^3 x 3 x 103 x 107 and N, which is given to be 2^3 x 3^2 x 5 x 103 x 107. We are also given that the GCF of 2,472 1,284, and N is 12. Recall that for any two positive integers a and b, we have a x b = LCM(a, b) x GCF(a, b). Therefore, by letting a = 2^3 x 3 x 103 x 107 and b = N, we have: 2^3 x 3 x 103 x 107 x N = 2^3 x 3^2 x 5 x 103 x 107 x 12 N = 3 x 5 x 12 N = 2^2 x 3^2 x 5 Answer: C
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Re: If the highest common factor of 2,472, 1,284 and positive integer N is
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01 Dec 2019, 06:15
chetan2u wrote: Bunuel wrote: 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\(2472=2*2*2*3*103=2^3*3*103\). \(1284=2*2*3*107=2^2*3*107\). 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?'Hi, Can you plz explain why cant we follow the method: HCF * LCM = Product of numbers? If we use that, it results in N=15



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Re: If the highest common factor of 2,472, 1,284 and positive integer N is
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01 Dec 2019, 07:46
ScottTargetTestPrep wrote: Bunuel wrote: 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 QuestionsRecall that for any two positive integers a and b, we have a x b = LCM(a, b) x GCF(a, b). Therefore, by letting a = 2^3 x 3 x 103 x 107 and b = N, we have: 2^3 x 3 x 103 x 107 x N = 2^3 x 3^2 x 5 x 103 x 107 x 12 N = 3 x 5 x 12 N = 2^2 x 3^2 x 5 Answer: C can you explain the bold line? 2472 x 1284 x N = (2^3 x 3 x 103) x (2^2 x 3 x 107) x N arnt you missing a few terms?



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Re: If the highest common factor of 2,472, 1,284 and positive integer N is
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03 Dec 2019, 20:15
Mansoor50 wrote: can you explain the bold line?
2472 x 1284 x N = (2^3 x 3 x 103) x (2^2 x 3 x 107) x N
arnt you missing a few terms?
I did not intend to multiply all three numbers together; as a matter of fact, when you have more than two numbers, the formula a x b = LCM(a, b) x GCF(a, b) is no longer valid. We are taking a = LCM(2472, 1284) and b = N and applying the formula to these numbers.
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Re: If the highest common factor of 2,472, 1,284 and positive integer N is
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05 Dec 2019, 07:17
ScottTargetTestPrep wrote: Mansoor50 wrote: can you explain the bold line?
2472 x 1284 x N = (2^3 x 3 x 103) x (2^2 x 3 x 107) x N
arnt you missing a few terms?
I did not intend to multiply all three numbers together; as a matter of fact, when you have more than two numbers, the formula a x b = LCM(a, b) x GCF(a, b) is no longer valid. We are taking a = LCM(2472, 1284) and b = N and applying the formula to these numbers. WOOT!......THANKS!!!!!




Re: If the highest common factor of 2,472, 1,284 and positive integer N is
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05 Dec 2019, 07:17






