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25 Nov 2019, 03:44
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (01:58) correct
69%
(02:04)
wrong
based on 128
sessions
History
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Not Attempted Yet
The least common multiple of N distinct natural numbers is 2520. Which of the following best describes N?
(A) 1 ≤ N ≤ 10
(B) 1 < N < 24
(C) 1 < N ≤ 40
(D) 1 ≤ N < 45
(E) 1 ≤ N < 50
(A) 1 ≤ N ≤ 10
(B) 1 < N < 24
(C) 1 < N ≤ 40
(D) 1 ≤ N < 45
(E) 1 ≤ N < 50
27 Nov 2019, 08:30
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CaptainLevi
Reasoning :
If the LCM of say a, b, c and d is x, then all these a, b, c and d are factors of x.
Now let me explain through a smaller number ..
If 36 is the number.... It can be LCM(6, 36), or LCM(2,4,9) and so on..
MIN :- SO the minimum number will be when there are ONLY 2 that is LCM(1,36) or (4,9) and so on.
MAX :- But what about the maximum number? It will be when we find LCM of all factors of 36 = LCM(1, 2, 3, 4, 6, 9, 12, 18, 36) =9 numbers, which is the number of factors calculated by \(36=2^2*3^2\)....# of factors = 3*3=9
The MAXIMUM value of N is when the largest number is 2520 and rest all its factors..
\(2520=2*2*2*3*3*5*7=2^3*3^2*5*7\)..
Number of factors = \((3+1)(2+1)(1+1)(1+1)=4*3*2*2=48\).
48 is part of ONLY E
E
29 Apr 2020, 23:38
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chetan2u
Hi,
Could you please explain why did you calculate total number of factors ?
