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What is the LCM of n C1 and n C2, where n is odd?
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Bunuel
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What is the LCM of n C1 and n C2, where n is odd? [#permalink] New post  15 Jun 2021, 05:00
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47% (01:11) correct 53% (01:28) wrong based on 70 sessions

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What is the LCM of nC1 and nC2, where n is an odd integer greater than 2?

(A) n

(B) n(n - 1)/2

(C) (n - 1)/2

(D) n/2

(E) n − 1
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Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
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abuc0112
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Re: What is the LCM of n C1 and n C2, where n is odd? [#permalink] New post  15 Jun 2021, 05:20
Answer: A
Any odd number greater than 2 would work.
Let n=3
3C1 = 3!/(2!*1!)
= 3
3C2 = 3!(2!*1!)
= 3
Since n =3, then the LCM of nC1 and nC2 = n

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VermaPulkit
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Re: What is the LCM of n C1 and n C2, where n is odd? [#permalink] New post  15 Jun 2021, 08:29
abuc0112 wrote:
Answer: A
Any odd number greater than 2 would work.
Let n=3
3C1 = 3!/(2!*1!)
= 3
3C2 = 3!(2!*1!)
= 3
Since n =3, then the LCM of nC1 and nC2 = n

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Can you please check with other odd numbers such as 5 or 7, you may not find that LCM is 5 or 7.

It seems LCM will be nC2, option B, I may be wrong but n doesn’t seem to be the right answer.
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nigamwadhwa100
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Re: What is the LCM of n C1 and n C2, where n is odd? [#permalink] New post  15 Jun 2021, 10:53
Answer should be B substitute 3 5 and 7 to find out.
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eddrm
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Re: What is the LCM of n C1 and n C2, where n is odd? [#permalink] New post  18 Jun 2021, 06:58
nC1=n!/(n-1)!=n
nC2=n!/(2*(n-2)!)=n*(n-1)/2

(A): n/nC1= n/n=1 OK
n/nC2=2(n-1), and since n is odd integer greater than 2, n>3. 2/(3-1)=1, 2/(5-1)=1/2 NOT OK.

(B) n(n-1)/2/nC1=(n-1)/2 OK
n(n-1)/2/nC2=1 OK

(C) doesn't work

(D) doesn't work

(E) doesn't work
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PSP92
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Re: What is the LCM of n C1 and n C2, where n is odd? [#permalink] New post  30 Jun 2021, 04:02
nC1= n and nC2=n(n - 1)/2
We see that nC2 is a multiple of nC1.
The LCM of two numbers where one is the multiple of the other, is the larger number.
For eg: The LCM of 12 and 48 is 48.
We know that (n - 1)/2 is greater than 1 as n is greater than 2. Therefore, n(n - 1)/2 is greater than n and hence the answer.
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Re: What is the LCM of n C1 and n C2, where n is odd? [#permalink]
30 Jun 2021, 04:02
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