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# The least common multiple of N distinct natural numbers is 2520. Which

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Manager
Joined: 18 Jul 2019
Posts: 54
The least common multiple of N distinct natural numbers is 2520. Which  [#permalink]

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25 Nov 2019, 03:44
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Difficulty:

55% (hard)

Question Stats:

48% (02:05) correct 52% (02:17) wrong based on 23 sessions

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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
Math Expert
Joined: 02 Aug 2009
Posts: 8289
The least common multiple of N distinct natural numbers is 2520. Which  [#permalink]

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27 Nov 2019, 08:30
CaptainLevi wrote:
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

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
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The least common multiple of N distinct natural numbers is 2520. Which   [#permalink] 27 Nov 2019, 08:30
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