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# Is x and y are positive integers, what is the value of xy?

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Manager
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Is x and y are positive integers, what is the value of xy? [#permalink]

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26 Apr 2008, 08:24
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Is x and y are positive integers, what is the value of xy?

(i) The greatest common factor of x and y is 10
(ii) The least common multiple of x and y is 180
Current Student
Joined: 28 Dec 2004
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Re: DS - greatest common factor and least common multiple [#permalink]

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26 Apr 2008, 08:55
quiet888 wrote:
Is x and y are positive integers, what is the value of xy?

(i) The greatest common factor of x and y is 10
(ii) The least common multiple of x and y is 180

these question ans choice is always either C or E..

lets see..

xy?
1)
gcd is 10

x=10 y=20
GCD =10 xy=200
x=10 y=60
GCD=10, xy=600

2)
LCM
x=180 y=2 LCM=180 xy=360
x=180 y=180 LCM=180 xy=180^2
Insuf

together
suppose x=180 y=10

suppse x=90 y=20

xy= is the same..Sufficient C it is.
Current Student
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Re: DS - greatest common factor and least common multiple [#permalink]

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26 Apr 2008, 11:50
another thing..with these type of question where we have the GCD and LCM..usually we can tell something like an XY but we cant really tell what X is or what y is...
Director
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Re: DS - greatest common factor and least common multiple [#permalink]

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27 Apr 2008, 14:27
anyway to solve this in under 2mins? fresh?
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Re: DS - greatest common factor and least common multiple [#permalink]

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27 Apr 2008, 19:17
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jimmyjamesdonkey wrote:
anyway to solve this in under 2mins? fresh?

Yes, even under 20 seconds if you remember that xy = GCD*LCM. Sure!
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Re: DS - greatest common factor and least common multiple [#permalink]

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28 Apr 2008, 07:25
Woah can you elaborate that a little bit...I always have such problems with GCF & LCM..
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Re: DS - greatest common factor and least common multiple [#permalink]

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19 Jul 2011, 00:30
FN wrote:
quiet888 wrote:
Is x and y are positive integers, what is the value of xy?

(i) The greatest common factor of x and y is 10
(ii) The least common multiple of x and y is 180

these question ans choice is always either C or E..

lets see..

xy?
1)
gcd is 10

x=10 y=20
GCD =10 xy=200
x=10 y=60
GCD=10, xy=600

2)
LCM
x=180 y=2 LCM=180 xy=360
x=180 y=180 LCM=180 xy=180^2
Insuf

together
suppose x=180 y=10

suppse x=90 y=20

xy= is the same..Sufficient C it is.

hi, For (ii) The least common multiple of x and y is 180
isn't x*y = 5400?

my rational...

if 180 is the Lowest Common Multiple, meaning that both x and y have 3, 3, 5, 2, 2 at least appeared twice for x y.

So if

x = 2, ?, 3, 5
y = 2, ?, 3, 5
-------------
x & y's LCM which is 180 = 2* 3* 5* ?* ?*

So after pulling 5 & 3 & 2, we still need one 2 and one 3 to fulfil the 3, 3, 5, 2, 2 = (180) requirement. Having said that, the ? in each x & y should be 2 and 3.

So multiple all 8 digits, it should x*y = 2* 2* 3* 5* 2* 3*3* 5* = 5400?
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Re: DS - greatest common factor and least common multiple [#permalink]

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01 Aug 2011, 08:31
Could some body help me to understand this a little better.

here is where I am getting stuck

GCF = 10, There for X = 10A nd Y = 10B where A and B are separate constants

for example 20 and 30, here the GDF is 10 and a = 2 and b = 3

sice we dont have a and b from this equation. this is insufficient

statement 2:

LCM is 180
so X*N1 = 180 and Y * N2 = 180

since we do not know the values of N1 and N2 this statement is not sufficient.

even if we combine, we dont have information to solve.

I see come body explaining the answer are LCM*GCD. Could you please tell me how you arrived at that equation
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Re: DS - greatest common factor and least common multiple [#permalink]

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01 Aug 2011, 09:38
GCF * LCM = X*Y it's a general rule
10*180 = 1800
so the the answer is C and u need less than 10 seconds

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Re: DS - greatest common factor and least common multiple [#permalink]

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01 Aug 2011, 10:04
Always; if we multiply two positive integers then the multiplication is same as the multiplication of their lcm and gcf. In this case lcm = 180 and gcf = 10 hence xy = (lcm)(gcf) = 180.10 = 1800
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Re: DS - greatest common factor and least common multiple [#permalink]

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02 Aug 2011, 10:44
manishgeorge wrote:
Could some body help me to understand this a little better.

here is where I am getting stuck

GCF = 10, There for X = 10A nd Y = 10B where A and B are separate constants

for example 20 and 30, here the GDF is 10 and a = 2 and b = 3

sice we dont have a and b from this equation. this is insufficient

statement 2:

LCM is 180
so X*N1 = 180 and Y * N2 = 180

since we do not know the values of N1 and N2 this statement is not sufficient.

even if we combine, we dont have information to solve.

I see come body explaining the answer are LCM*GCD. Could you please tell me how you arrived at that equation

it's a general rule and can always applied .
if u want the details about how we arrived at that equation just let me know
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How can i lose my faith in life's fairness when i know that the dreams of those who sleep on the feathers are not more beautiful than the dreams of those who sleep on the ground? - Jubran Khaleel Jubran

Re: DS - greatest common factor and least common multiple   [#permalink] 02 Aug 2011, 10:44
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