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GCD AND LCM of Fractions

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zaarathelab
 Post subject: GCD AND LCM of Fractions
 Post Posted: Sun Sep 04, 2011 12:42 pm 
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Students


Posts: 11
Hi I read somewhere that one can calculate the LCM and HCF of fractions using the below mentioned principle -

LCM OF a/b and c/d =
LCM OF Numerators (a and c)/ HCF of denominators (b and d)

Similarily,

HCF of a/b and c/d =

HCF of Numerators(a and c)/ LCM of denominators (b and d)

Is this correct or is there any other approach?

Coz,

if i find the LCM of 5/3 and 7/11 by this rule I get it = 35 which is plain wrong as 35 is not a multiple of 5/3 and 7/11

Experts, pls tell me if we can calculate the LCM and HCF of fractions

Thanks
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JohnHarris
 Post subject: Re: GCD AND LCM of Fractions
 Post Posted: Sun Sep 04, 2011 8:09 pm 
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Forum Guests


Posts: 38
zaarathelab wrote:
Hi I read somewhere that one can calculate the LCM and HCF of fractions using the below mentioned principle - ...


I have a pretty good handle on what the least common multiple (LCM) of two rational number are but I'm confused on the highest common factor (HCF). How is a factor of a rational number defined? I can think of several but, in a quick look around the web, I didn't see one.

One of the reasons I ask is that by both Euclid's algorithm and other methods, defining factors of a rational number R as the set (R/n; n = 1, 2, 3, ...), I get the HCF(5/3, 7/11) is 1/33 but a higher common factor is 1

Oh, and BTW,
35 = 21 * 5/3
and
35 = 55 * 7/11
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tim
 Post subject: Re: GCD AND LCM of Fractions
 Post Posted: Tue Oct 04, 2011 12:34 am 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
Hi John,
No you didn’t miss the memo on this one. Defining an LCM or HCF of things that aren’t integers is dubious at best, at least according to the ordinary definitions of factors and multiples. I see some merit in your definition, although I will point out that 1/33 would be the HCF – although 1 is higher, 1 is a factor of neither of those numbers (if you disagree, it means we are using different definitions for one or more of our terms). Fortunately, these issues WILL NOT show up on the GMAT..

_________________
Tim Sanders
Manhattan GMAT Instructor
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