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greatest common divisor - confused????

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by Gurpinder » Tue Dec 15, 2009 9:21 am
hey guys,

i was reviewing for the gmat and was learning about the greatest common divisor stuff and came came across this question:

Which number is the greatest common divisor (GCD) of 45 and 75?
A. 3,375
B. 225
C. 15
D. 5
E. 3

my answer, after doing prime factorization was 15. the book says the answer is 225 :S:S:S howww?!?!?!?!
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by Hussain15 » Tue Dec 15, 2009 9:27 am
There must be a typo in the book, ur answer is correct.
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by Gurpinder » Tue Dec 15, 2009 9:30 am
right????? thats what i have been thinkingg

because 225 is the LEAST COMMON MULTIPLE not the GC divisor.

hmmmm ok

thanks for ur reply!
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by tata » Wed Dec 16, 2009 12:19 pm
Gurpinder wrote:right????? thats what i have been thinkingg

because 225 is the LEAST COMMON MULTIPLE not the GC divisor.

hmmmm ok

thanks for ur reply!
No its the other way round, the LCM is 15 and the GCD is 225, OA is correct.
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by kabirmohammed » Wed Dec 16, 2009 1:18 pm
Multiples of 45: 45, 90, 135, 180, 225, 270,.......
Multiples of 75: 75, 150, 225, 300, .....
from the above multiples the Least common multiple(LCM) is 225

GCD of a,b = axb/(lcm(a,b)
= 45x75/225
=15
correct me if iam wrong..
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by nittanylion530 » Wed Dec 16, 2009 1:24 pm
Tata is correct. You are thinking about it backwards. LCM is 15 and GCD is 225.
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by Gurpinder » Wed Dec 16, 2009 1:44 pm
ummm noo....kabirmohamed is right.....gcd is 15.....lcm is 225
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by nittanylion530 » Wed Dec 16, 2009 2:25 pm
What's the source of this question?
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by Ian Stewart » Wed Dec 16, 2009 4:37 pm
Some confusion in the posts above! The least common multiple of two numbers must be a multiple of both numbers; it will normally be larger than both numbers (occasionally it will be equal to the larger of the two). The LCM of 45 and 75 is 225.

The greatest common divisor of two numbers must be a divisor/factor of both numbers; it will normally be smaller than both numbers (occasionally it will be equal to the smaller of the two). The GCD of 45 and 75 is 15.

Any book that claims the GCD of 45 and 75 is 225 should probably be thrown in the bin! Which book is it, by the way?
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by Lattefah84 » Thu Dec 17, 2009 12:19 am
Ian Stewart wrote:Some confusion in the posts above! The least common multiple of two numbers must be a multiple of both numbers; it will normally be larger than both numbers (occasionally it will be equal to the larger of the two). The LCM of 45 and 75 is 225.

The greatest common divisor of two numbers must be a divisor/factor of both numbers; it will normally be smaller than both numbers (occasionally it will be equal to the smaller of the two). The GCD of 45 and 75 is 15.

Any book that claims the GCD of 45 and 75 is 225 should probably be thrown in the bin! Which book is it, by the way?
I agree.
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