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# If x is the greatest common divisor of 90 and 18, and y is the least

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If x is the greatest common divisor of 90 and 18, and y is the least  [#permalink]

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17 Oct 2018, 01:21
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Difficulty:

25% (medium)

Question Stats:

77% (01:32) correct 23% (01:53) wrong based on 87 sessions

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If x is the greatest common divisor of 90 and 18, and y is the least common multiple of 51 and 34, then x + y =

A. 111
B. 120
C. 213
D. 222
E. 231

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Re: If x is the greatest common divisor of 90 and 18, and y is the least  [#permalink]

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17 Oct 2018, 01:51
Finding x - GCD (90 ,18)
90 = 2 x $$3^2$$ x 5
18 = 2 x $$3^2$$

--> x = 2 x $$3^2$$ = 18

Finding y - LCM (51,34)
51 = 3 x 17
34 = 2 x 17

--> y = 2 x 3 x 17 = 102

--> x + y = 102 + 18 = 120

--> Option B is the answer

Let me know your thought. Thank you
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Re: If x is the greatest common divisor of 90 and 18, and y is the least  [#permalink]

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17 Oct 2018, 01:52
Bunuel wrote:
If x is the greatest common divisor of 90 and 18, and y is the least common multiple of 51 and 34, then x + y =

A. 111
B. 120
C. 213
D. 222
E. 231

To find the GCD and LCM of two numbers always denote the numbers in the prime factorization form -

First pair:
$$18 = 2^1*3^2$$
$$90 = 2^1*3^2*5^1$$

To find GCD of these two numbers - find the common factors ( along with powers) : So GCD would be : $$2^1*3^2 = 18$$

Second pair:

$$51 = 3^1*17^1$$
$$34 = 2^1*17^1$$

So GCD is $$17^1 = 17$$ and the LCM is (First number * Second number)/GCD = $$\frac{(3^1*17^1*2^1*17^1)}{17^1} =$$$$3*2*17$$

Hence the question is asking $$18 + 6*17 = 18 + 102 = 120$$

Hence Option (B) is our choice.

Regards,
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Re: If x is the greatest common divisor of 90 and 18, and y is the least  [#permalink]

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17 Oct 2018, 01:55
Bunuel wrote:
If x is the greatest common divisor of 90 and 18, and y is the least common multiple of 51 and 34, then x + y =

A. 111
B. 120
C. 213
D. 222
E. 231

If x is the greatest common divisor of 90 and 18 then x=18

And y is the least common multiple of 51 and 34 then y=102

x+y = 18+102 = 120

Hence B
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Re: If x is the greatest common divisor of 90 and 18, and y is the least  [#permalink]

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18 Oct 2018, 18:29
Bunuel wrote:
If x is the greatest common divisor of 90 and 18, and y is the least common multiple of 51 and 34, then x + y =

A. 111
B. 120
C. 213
D. 222
E. 231

Factoring 18 and 90, we get: 18 = 9 x 2 = 2 x 3^2 and 90 = 9 x 10 = 2 x 3^2 x 5

The GCF of 18 and 90 is 2 x 3^2 = 18. This is the value of x.

Factoring 51 and 34, we get: 51 = 3 x 17 and 34 = 2 x 17

The LCM of 51 and 34 is 17 x 2 x 3 = 102. This is the value of y.

Thus, the sum of x and y is 18 + 102 = 120.

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Re: If x is the greatest common divisor of 90 and 18, and y is the least   [#permalink] 18 Oct 2018, 18:29
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