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If x represents the Least Common Multiple of 12 and 18, and

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by BTGmoderatorDC » Wed Sep 26, 2018 6:33 pm

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If x represents the Least Common Multiple of 12 and 18, and y represents the Greatest Common Factor of 12 and 18, what is the value of x−y ?

A. 20
B. 24
C. 30
D. 34
E. 210

OA C

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by deloitte247 » Wed Sep 26, 2018 10:11 pm
The LCM of 12 and 18 is 36. So, X=36

HCF 12 and 18
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 18 are : 1, 2, 3, 6, 9, 18
The common factors here are 1, 2, 3 and 6. Thus, the HCF is 6. Therefore, Y=6

The value of X - Y= 36-6 = 30
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by Scott@TargetTestPrep » Tue Oct 09, 2018 9:43 am
BTGmoderatorDC wrote:If x represents the Least Common Multiple of 12 and 18, and y represents the Greatest Common Factor of 12 and 18, what is the value of x−y ?

A. 20
B. 24
C. 30
D. 34
E. 210
The LCM of 12 and 18 is 36. We see that 12 = 2^2 x 3 and 18 = 2 x 3^2. The LCM is the product of the greatest number of 2s and the greatest number of 3s appearing in either factorization; thus, we see that the LCM of 12 and 18 is 2^2 x 3^2, or 36.

The GCF of 12 and 18 is 6. Using the prime factorization from above, we need the product of the smallest number of 2s and the smallest number of 3s appearing in both factorizations; thus, we see that the GCF of 12 and 18 is 2 x 3 = 6.

Thus, x - y = 36 - 6 = 30.

Answer: C

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