 # Find the HCF and LCM of Question:

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

Solution:

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

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

Prime factorisation of the numbers given in the numerators are as follows:

$8=2 \times 2 \times 2$

$10=2 \times 5$

$16=2 \times 2 \times 2 \times 2$

HCF of Numerators $=2$

$L C M$ of Numerators $=2^{4} \times 5=80$

Prime factorisation of numbers given in the denominators are as follows:

$9=3 \times 3$

$27=3 \times 3 \times 3$

$81=3 \times 3 \times 3 \times 3$

HCF of Denominators $=3 \times 3=9$

$L C M$ of Denominators $=3^{4}=81$

$\therefore \mathrm{HCF}$ of fractions $=\frac{\mathrm{HCF} \text { of Numerator }}{\mathrm{LCM} \text { of Denominator }}=\frac{2}{81}$

$\therefore \mathrm{LCM}$ of fractions $=\frac{\text { LCM of Numerator }}{\text { HCF of Denominator }}=\frac{80}{9}$