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Re: gcf and lcm problem [#permalink]
04 Jun 2009, 23:56

1

This post received KUDOS

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

ANSWER: C.

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

Re: gcf and lcm problem [#permalink]
05 Jun 2009, 02:41

2

This post received KUDOS

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

Re: gcf and lcm problem [#permalink]
05 Jun 2009, 05:07

1

This post received KUDOS

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

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.

Re: gcf and lcm problem [#permalink]
05 Jun 2009, 22:39

1

This post received KUDOS

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