LCM and GCD/HCF of fractions

Expert replies

zaarathelab: Master | Next Rank: 500 Posts; Posts: 217; Joined: Sun Jan 10, 2010 1:39 pmFollowed by: 1 member; Thanked: 7 times

by zaarathelab » Sun Sep 04, 2011 8:38 am

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

Source: Beat The GMAT — Problem Solving | Sun Sep 04, 2011 8:38 am

sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Sun Sep 04, 2011 9:08 am

Those formulae are correct. Also, the answer to your example is correct. You should not be checking the result against the fraction, as only the numerators of both fractions are multiples of 35. The denominator is the HCF of those fractions

zaarathelab: Master | Next Rank: 500 Posts; Posts: 217; Joined: Sun Jan 10, 2010 1:39 pmFollowed by: 1 member; Thanked: 7 times

by zaarathelab » Sun Sep 04, 2011 12:06 pm

Yes, but then how can 35 be a multiple of 5/3?? Doesn't it defy the LCM principle?

prashant.mishra: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Thu Jul 14, 2011 9:41 am; Thanked: 9 times; GMAT Score:650

by prashant.mishra » Mon Sep 05, 2011 9:32 pm

No it does not... The formulae are correct. 35 is indeed a multiple of 5/3. To find the factor divide 35/(5/3). You get 21. conversely, multiply 21 by 5/3.. 5/3*21 = 35. Similarly, 35/(7/11) gives 55. Conversely, 55*7/11= 35.

Hope this helps.

zaarathelab wrote:Yes, but then how can 35 be a multiple of 5/3?? Doesn't it defy the LCM principle?

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Sep 06, 2011 1:12 pm

You will never need to be concerned with finding the LCM or GCD of fractions on the GMAT. You only need to understand what those concepts mean for positive integers.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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