Discussion
H. C. F. of \(\frac{4}{9}\), \(\frac{10}{21}\) and \(\frac{20}{63}\) is
Answer: C
The H.C.F. is \(\frac{2}{63}\).
The H.C.F. of fractions is the H.C.F. of the numerators divided by the L.C.M. of the denominators:
\[ \begin{aligned} \text{HCF}(4, 10, 20) &= 2 \\ \text{LCM}(9, 21, 63) &= 63 \end{aligned} \]
So the H.C.F. is \(\frac{2}{63}\). Each fraction is a whole-number multiple of it: \(\frac{4}{9} = 14 \times \frac{2}{63}\), \(\frac{10}{21} = 15 \times \frac{2}{63}\) and \(\frac{20}{63} = 10 \times \frac{2}{63}\). \(\frac{1}{21}\) and \(\frac{5}{63}\) do not divide all three exactly.
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