Question

Find the HCF and LCM of $\frac{8}{9},\frac{10}{27}$ and $\frac{16}{81}$.

Answer 1

$\mathrm{HCF}\mathrm{of}\mathrm{fractions}=\frac{\mathrm{HCF}\mathrm{of}\mathrm{Numerators}}{\mathrm{LCM}\mathrm{of}\mathrm{Denominators}}$

$\mathrm{LCM}\mathrm{of}\mathrm{fractions}=\frac{\mathrm{LCM}\mathrm{of}\mathrm{Numerators}}{\mathrm{HCF}\mathrm{of}\mathrm{Denominators}}$
Prime factorisation of the numbers given in the numerators are as follows:
$$\begin{gathered} 8=2\times 2\times 2 \\ 10=2\times 5 \\ 16=2\times 2\times 2\times 2 \end{gathered}$$

$HCFofNumerators=2$
$LCMofNumerators=2^4\times 5$ = $80$

Prime factorisation of numbers given in the denominators are as follows:
$$\begin{gathered} 9=3\times 3 \\ 27=3\times 3\times 3 \\ 81=3\times 3\times 3\times 3 \end{gathered}$$

$HCFofDenominators=3\times 3=9$
$LCMofDenominators=3^4=81$


∴ $\mathrm{HCF}\mathrm{of}\mathrm{fractions}=\frac{\mathrm{HCF}\mathrm{of}\mathrm{Numerator}}{\mathrm{LCM}\hspace{0.17em}\mathrm{of}\mathrm{Denominator}}=\frac{2}{81}$

∴ $\mathrm{LCM}\hspace{0.17em}\mathrm{of}\mathrm{fractions}=\frac{\mathrm{LCM}\hspace{0.17em}\mathrm{of}\mathrm{Numerator}}{\mathrm{HCF}\mathrm{of}\mathrm{Denominator}}=$$\frac{80}{9}$