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scorpio7
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gcf and lcm problem 04 Jun 2009, 21:41
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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

ANSWER: C.



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gcf and lcm problem 05 Jun 2009, 00:56
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scorpio7
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.
Show more

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
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gcf and lcm problem 05 Jun 2009, 02:41
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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
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gcf and lcm problem 05 Jun 2009, 03:41
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bigtreezl

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
Show more
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 https://www.purplemath.com/modules/lcm_gcf.htm
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joyseychow
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gcf and lcm problem 05 Jun 2009, 06:07
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humans
bigtreezl

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 https://www.purplemath.com/modules/lcm_gcf.htm
Show more

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.

Answer is definitely C.
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ALD
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gcf and lcm problem 05 Jun 2009, 09:58
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the answer should be C.
the product of 2 number= product of their Lcm and HCF
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gcf and lcm problem 05 Jun 2009, 23:39
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humans
bigtreezl

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 https://www.purplemath.com/modules/lcm_gcf.htm
Show more

yeah..you're right..makes perfect sense

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gcf and lcm problem 31 Oct 2018, 15:05
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