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Bunuel
What is the value of integer x?
The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\).

One thing I have always wondered to know, does this rule apply for multiple numbers or only when you have two numbers? Thanks.
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Bunuel
What is the value of integer x?

(1) The lowest common multiple of x and 16 is 48 --> x can be 3, 6, 12, 24, or 48. Not sufficient.

(2) The greatest common factor of x and 16 is 4 --> x can take more than one value, for example, 4, 12, 20, .. (basically any number of the form 4*odd). Not sufficient.

(1)+(2) The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\). According to this 16x=48*4 --> x=12. Sufficient.

Answer: C.



this is the best explanation I have heard so far) even my tutor from Veritas prep can't solve it today:(
thinking maybe i need to change my tutor?:)
btw-it so sad that you don't provide tutoring:(
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3111987
What is the value of integer x?

(1) The lowest common multiple of x and 16 is 48.
(2) The greatest common factor of x and 16 is 4

have no idea why the answer is not E,cause
from (1) i have ...6->12->24
from (2) i have ...4->12->24
thanks for explanation;)

this question from Veritas prep:)

1. The answer is c
LCM(x,y) *GCM(x*y) =xy
so 48*4 = 16 *x
on solving x=12.
now you can cross verify
LCM(12,16) =48
GCM(12,16)=4
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Bunuel
What is the value of integer x?
The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\).

One thing I have always wondered to know, does this rule apply for multiple numbers or only when you have two numbers? Thanks.

Check a simple example:

GCD(6, 10, 12) = 2;
LCM(6, 10, 12) = 60;

6*10*12 = 720, while GCD(6, 10, 12)*LCM(6, 10, 12) = 120.

Hope it's clear.
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Bunuel
What is the value of integer x?

(1) The lowest common multiple of x and 16 is 48 --> x can be 3, 6, 12, 24, or 48. Not sufficient.

(2) The greatest common factor of x and 16 is 4 --> x can take more than one value, for example, 4, 12, 20, .. (basically any number of the form 4*odd). Not sufficient.

(1)+(2) The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\). According to this 16x=48*4 --> x=12. Sufficient.

Answer: C.

Hello Bunuel,

Could you explain this part in red please? Why 4*odd?

Thank you.
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Bunuel
What is the value of integer x?

(1) The lowest common multiple of x and 16 is 48 --> x can be 3, 6, 12, 24, or 48. Not sufficient.

(2) The greatest common factor of x and 16 is 4 --> x can take more than one value, for example, 4, 12, 20, .. (basically any number of the form 4*odd). Not sufficient.

(1)+(2) The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\). According to this 16x=48*4 --> x=12. Sufficient.

Answer: C.

Hello Bunuel,

Could you explain this part in red please? Why 4*odd?

Thank you.

Since the greatest common factor of x and 16 = 2^4 is 4 = 2^2, then x cannot have 2 in higher power than 2, hence 4*odd.
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Excellent Question.
Here is what i did in this one -->
We need the value of integer x.
Statement 1-->
LCM(x,16)=48
Hence the possible values of x -->
3
3*2
3*2^2
3*2^3
3*2^4
Hence not sufficient.
Statement 2->
GCD(x,16)=4
Hence the general Expression for x will be => x=2^2*k where x is any odd number.
Hence not sufficient.

Combing the two statements->
x must be 3*2^2
Hence sufficient.

Hence C.
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What is the value of integer x?

(1) The lowest common multiple of x and 16 is 48.

The prime factorization of 16 is 2^4. If the LCM common multiple of x and 16 is 48, this tells us x consists of a 3. However, we don't know what else the 3 contains. X could be 3, 6, 48, etc. Insufficient.

(2) The greatest common factor of x and 16 is 4

The GCF of x and 16 is 2^2. X could be 20, 28, etc. Insufficient.

(1&2) GCF * LCM = 192
192 / 16 = 12
X = 12

Answer is C.
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