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If the LCM of two integers a, b (where b> a and a>1) is a*b, then whi

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If the LCM of two integers a, b (where b> a and a>1) is a*b, then whi  [#permalink]

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New post 19 Nov 2014, 00:44
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If the LCM of two integers a, b (where b> a and a>1) is a*b, then which of the following can not be true?

A. Both a and b can be Prime Numbers.
B. Both a and b can be consecutive integers.
C. All Prime factors of a must be Prime factors of b.
D. a and b do not share any Prime factors.
E. a and b do not have a common factor
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Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whi  [#permalink]

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New post 19 Nov 2014, 01:04
manpreetsingh86 wrote:
If the LCM of two integers a, b (where b> a and a>1) is a*b, then which of the following can not be true?

A. Both a and b can be Prime Numbers.
B. Both a and b can be consecutive integers.
C. All Prime factors of a must be Prime factors of b.
D. a and b do not share any Prime factors.
E. a and b do not have a common factor



Say a = 2; b = 3; only option C contradicts

All Prime factors of a must be Prime factors of b

Answer = C
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Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whi  [#permalink]

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New post 20 Nov 2014, 08:01
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manpreetsingh86 wrote:
If the LCM of two integers a, b (where b> a and a>1) is a*b, then which of the following can not be true?

A. Both a and b can be Prime Numbers.
B. Both a and b can be consecutive integers.
C. All Prime factors of a must be Prime factors of b.
D. a and b do not share any Prime factors.
E. a and b do not have a common factor



If LCM of two numbers A and B is the product AB then both numbers are Co- prime.

( Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).

Numbers that can be Co-Prime are :

1) Two consecutive natural numbers.
2) Two consecutive odd numbers.
3) Two prime numbers.
4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.

With above four statements it can be concluded that Options A, B, D and E are all true.

Only Option C cannot be true.
Hence answer is C
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If the LCM of two integers a, b (where b> a and a>1) is a*b, then whi  [#permalink]

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New post 18 Mar 2016, 03:06
a*b=LCM*GCF

a*b=LCM means GCF=1, so a and b are coprime numbers, i.e. do not share any factor except 1

C cannot be true
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Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whi  [#permalink]

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New post 20 Dec 2016, 07:03
manpreetsingh86 wrote:
If the LCM of two integers a, b (where b> a and a>1) is a*b, then which of the following can not be true?

A. Both a and b can be Prime Numbers.
B. Both a and b can be consecutive integers.
C. All Prime factors of a must be Prime factors of b.
D. a and b do not share any Prime factors.
E. a and b do not have a common factor


By definition, co-prime numbers are numbers which don't share any common factor EXCEPT 1 or which GCF is 1. C is fits perfectly but what about E?
We have: "a and b do not have a common factor". Co-primes don't share any prime factor, but they DO SHARE one common factor and that factor is 1. Hence E fits the bill too.
Can anybody clarify this, please.
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Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whi  [#permalink]

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Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whi &nbs [#permalink] 24 Feb 2018, 00:16
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