If x is the lowest common multiple of 15, 18, and 24 and y is the grea

Question

If x is the lowest common multiple of 15, 18, and 24 and y is the greatest common factor of 15, 18, and 24, what is the value of x^2 – 2xy + y^2?

A. 115^2 
B. 250^2 
C. 357^2 
D. 463^2 
E. 500^2

chetan2u · Accepted Answer

hi,

Two ways.. 
 1)straight elimination 
all terms 15, 18 and 24 are multiple of 3 and 9 in one number..
so their HCF, y and LCM, x should also be multiple of 3..
so all terms in  x^2 – 2xy + y^2  should be multiple of 3..
look for a choice which is a multiple of 3..
ONLY C is left

2)lets find the HCF and LCM first.. 
 15= 3*5....
18=2*3^2...
24=2^3*3..

HCF = 3..
LCM = 2^3*3^2*5

now 
 x^2 – 2xy + y^2 = (x-y)^2 = (2^3*3^2*5-3)^2=357^2 
C

sashaman14 · Answer

Your answer appears correct but your Greatest Common Factor isn't. I don't know how you got the answer correct given your work. you have 2*3^6*5...... it should be 5*3^2*2^3 (which equals 360).
Your GCF equals to 7290.
Also, 18 GCF is not 2*3^3..... it is 3^2*2

If you work it out, you will see that answer is (3-360)^2.... which is (-357)^2...which is in turn 357^2. Hope this helps

ronny123 · Answer

LCM of 
15 = 3 x 5 
18 = 3 x 3 x 2
24 = 3 x 2 x 2 x 2

is 3 x 2 x 5 x 3 x 2 x 2 = 360

GCF of 15, 18 and 24 = 3 (as seen above)

so X = 360 and Y =3

X^2 – 2XY + Y^2 = (X - Y)^2 = (360-3)^2 = 357^2

Correct Option : C

rohit8865 · Answer

i think highlighted part is wrong....

chetan2u · Answer

Hi,
 The answer is correct and GCF is also correct as 3.. 
However there are few typo in LCMs, which I have corrected..
 I have corrected the errors..

But you should not get confused in GCF and LCM..
GCF is HCF, which is the greatest common factor 
 
here these are not GCF BUT factors..

stonecold · Answer

Here its easy to get the GCD and the LCM 
LCM => 360
GCD=> 3

(x-y)^2=357^2 i.e option C

Abhishek009 · Answer

LCM (15, 18, 24) = 360
HCF (15, 18, 24) = 3

x^2 – 2xy + y^2 = (x - y)^2

Or,  x^2 – 2xy + y^2 = (360 - 3)^2 = 357^2 , Answer will be (C)

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If x is the lowest common multiple of 15, 18, and 24 and y is the grea

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