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I was reading a text book and came across the following approach to find the LCM and HCF of rational numbers/fractions:

  • LCM of fractions = LCM of numerators/HCF of denominators
  • HCF of fractions = HCF of numerators/LCM of denominators

Can someone please help me understand why the above formula holds true or how the above is logically deduced?

Thanks in advance!

  • 1
    I think you start with the observation that for integers $a, b, k$ we have $\gcd(ka, kb) = k \gcd(a, b)$ and $\text{lcm}(ka, kb) = k \text{lcm}(a, b)$ and then just extend this to rational $k$. You should get the same result as the above.2011-06-11
  • 0
    Which textbook is this?2016-07-03

4 Answers 4