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# gcf and lcm problem

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Intern
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04 Jun 2009, 20:41
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hey guys was wondering if someone could offer a way to solve this problem:

If X and Y are integers, what is the value of xy?

(1) The greates common factor of X and Y is 10

(2) The least common multiple of X and Y is 180

Director
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Re: gcf and lcm problem [#permalink]

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04 Jun 2009, 23:56
1
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scorpio7 wrote:
hey guys was wondering if someone could offer a way to solve this problem:

If X and Y are integers, what is the value of xy?

(1) The greates common factor of X and Y is 10

(2) The least common multiple of X and Y is 180

E

1) x and y could be a variety of numbers that include the primes 2 and 5
insuff
2) x and y could be a variety of numbers with prime factors that include 3,3,5,2,2 between the two

together
x and y must both contain 2 and 5, but there is only one 5 in 180
insufficient
Senior Manager
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Concentration: Technology, Marketing
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Re: gcf and lcm problem [#permalink]

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05 Jun 2009, 01:41
1)
x and y could be 20 ,30/30,40......any number with 2,5 as factors
insufficient

2)
x and y could be a variety of numbers with prime factors that include 3,3,5,2,2
iNSUFFIENT

TOGETHER

x and y must have 2,5 as factors ; however the remaining factors can be adjusted in many ways

iNSUFFIENT
IMO E
_________________

Lahoosaher

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Re: gcf and lcm problem [#permalink]

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05 Jun 2009, 02:41
2
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bigtreezl wrote:
E

1) x and y could be a variety of numbers that include the primes 2 and 5
insuff
2) x and y could be a variety of numbers with prime factors that include 3,3,5,2,2 between the two

together
x and y must both contain 2 and 5, but there is only one 5 in 180
insufficient

I think we can find the value of XY

Statement (1) says 2 and 5 are common factors of X and Y-------Insufficient
Statement (2) the LCM of X and Y is 180 which means 2,2,3,3, and 5 factors of X and Y-------Insufficient

Combining both the statements

2 5 2 3 3
2 5
-------------------------------------------------
GCF 2 x 5 = 10 (Greatest power of common multiples)
LCM 2 x 5 x 2 x 3 x 3 = 180 (Least power of all the multiples)

The only common primes between X and Y are 5, and 2. The remaining primes of LCM (2, 3, 3) will be primes of either X or Y and not both, because if it will be in both it will be multiplied to get the GCF.

The number in this case would be 180*10 = 1800. Hence C is the answer

Some good info on LCM and GCF http://www.purplemath.com/modules/lcm_gcf.htm
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Re: gcf and lcm problem [#permalink]

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05 Jun 2009, 05:07
1
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humans wrote:
bigtreezl wrote:
E

1) x and y could be a variety of numbers that include the primes 2 and 5
insuff
2) x and y could be a variety of numbers with prime factors that include 3,3,5,2,2 between the two

together
x and y must both contain 2 and 5, but there is only one 5 in 180
insufficient

I think we can find the value of XY

Statement (1) says 2 and 5 are common factors of X and Y-------Insufficient
Statement (2) the LCM of X and Y is 180 which means 2,2,3,3, and 5 factors of X and Y-------Insufficient

Combining both the statements

2 5 2 3 3
2 5
-------------------------------------------------
GCF 2 x 5 = 10 (Greatest power of common multiples)
LCM 2 x 5 x 2 x 3 x 3 = 180 (Least power of all the multiples)

The only common primes between X and Y are 5, and 2. The remaining primes of LCM (2, 3, 3) will be primes of either X or Y and not both, because if it will be in both it will be multiplied to get the GCF.

The number in this case would be 180*10 = 1800. Hence C is the answer

Some good info on LCM and GCF http://www.purplemath.com/modules/lcm_gcf.htm

I agree. One of the properties of GCF and LCM is (GCF of A and B) * (LCM of A and B) = A*B.
GCF consist of shared prime factors and LCM consist of non-shared prime factors. Together they both form the combined integer as demonstrated by humans.

Manager
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Re: gcf and lcm problem [#permalink]

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05 Jun 2009, 08:58
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the product of 2 number= product of their Lcm and HCF
Director
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Re: gcf and lcm problem [#permalink]

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05 Jun 2009, 22:39
1
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humans wrote:
bigtreezl wrote:
E

1) x and y could be a variety of numbers that include the primes 2 and 5
insuff
2) x and y could be a variety of numbers with prime factors that include 3,3,5,2,2 between the two

together
x and y must both contain 2 and 5, but there is only one 5 in 180
insufficient

I think we can find the value of XY

Statement (1) says 2 and 5 are common factors of X and Y-------Insufficient
Statement (2) the LCM of X and Y is 180 which means 2,2,3,3, and 5 factors of X and Y-------Insufficient

Combining both the statements

2 5 2 3 3
2 5
-------------------------------------------------
GCF 2 x 5 = 10 (Greatest power of common multiples)
LCM 2 x 5 x 2 x 3 x 3 = 180 (Least power of all the multiples)

The only common primes between X and Y are 5, and 2. The remaining primes of LCM (2, 3, 3) will be primes of either X or Y and not both, because if it will be in both it will be multiplied to get the GCF.

The number in this case would be 180*10 = 1800. Hence C is the answer

Some good info on LCM and GCF http://www.purplemath.com/modules/lcm_gcf.htm

yeah..you're right..makes perfect sense
Re: gcf and lcm problem   [#permalink] 05 Jun 2009, 22:39
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