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Math Expert V
Joined: 02 Sep 2009
Posts: 56257
If the LCM of two integers a, b (where b> a and a>1) is a*b, then whic  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (01:07) correct 22% (01:12) wrong based on 45 sessions

### HideShow timer Statistics 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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Senior Manager  G
Joined: 22 Nov 2018
Posts: 478
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whic  [#permalink]

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Bunuel 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

a*b=LCM(a,b)*HCF(a,b)
As per stem HCF = 1; So A,B,D,E are ruled out. IMO C
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Director  G
Joined: 20 Jul 2017
Posts: 544
Location: India
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Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whic  [#permalink]

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1
Bunuel 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

LCM of 2 numbers a & b = a*b is only possible if a & b have no common factors
or HCF(a, b) = 1

A. Both a and b can be Prime Numbers. - TRUE (No 2 prime numbers have common factors)
B. Both a and b can be consecutive integers. - TRUE (No 2 consecutive integers will have any common factors. Eg: (2, 3), (5, 6), (10, 11) etc.)
C. All Prime factors of a must be Prime factors of b. - NOT TRUE (There can't be any common factors, Either prime or non prime)
D. a and b do not share any Prime factors. - TRUE (There can't be any common factors)
E. a and b do not have a common factor - TRUE (As of D)

IMO Option C

Pls Hit Kudos if you like the solution
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Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whic  [#permalink]

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1
Dillesh4096, hello;

I'm a little confused with Statement E.
There is a possibility that 7 and 4 are the numbers and they have a common factor, 1. Kindly help!

Dillesh4096 wrote:
Bunuel 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

LCM of 2 numbers a & b = a*b is only possible if a & b have no common factors
or HCF(a, b) = 1

A. Both a and b can be Prime Numbers. - TRUE (No 2 prime numbers have common factors)
B. Both a and b can be consecutive integers. - TRUE (No 2 consecutive integers will have any common factors. Eg: (2, 3), (5, 6), (10, 11) etc.)
C. All Prime factors of a must be Prime factors of b. - NOT TRUE (There can't be any common factors, Either prime or non prime)
D. a and b do not share any Prime factors. - TRUE (There can't be any common factors)
E. a and b do not have a common factor - TRUE (As of D)

IMO Option C

Pls Hit Kudos if you like the solution

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Director  G
Joined: 20 Jul 2017
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Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whic  [#permalink]

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[quote="LeoN88"]Dillesh4096, hello;

I'm a little confused with Statement E.
There is a possibility that 7 and 4 are the numbers and they have a common factor, 1. Kindly help!

Hi LeoN88

It looks ambiguous as 1 is a common factor. I guess Option E should've been a and b do not have a common factor other than 1

Between option C & E, i think we should choose C

Guess, knowing the source will help further.

Bunuel Pls Guide Re: If the LCM of two integers a, b (where b> a and a>1) is a*b, then whic   [#permalink] 21 Jun 2019, 02:41
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