​​Find the HCF and LCM of 8/9,10/27 and 16/81. ​

Question

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

Answer 1

HCF of fractions = \(\frac{HCF\,of\,numerators}{LCM\,of\,denominators}\)

LCM of fractions = \(\frac{LCM\,of\,numerators}{HCF\,of\,denominators}\)

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

8 = 2 × 2 × 2 

10 = 2 × 5 

16 = 2 × 2 × 2 × 2 

HCF of numerators = 2 

LCM of numerators = 2⁴ × 5 = 80 

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

9 = 3 × 3

27 = 3 × 3 × 3 

81 = 3 × 3 × 3 × 3 

HCF of denominators = 3 × 3 = 9 

LCM of denominators = 3⁴ = 81

∴ HCF of fractions = \(\frac{HCF\,of\,numerators}{LCM\,of\,denominators}\) = \(\frac{2}{81}\)

∴ LCM of fractions = \(\frac{LCM\,of\,numerators}{HCF\,of\,denominators}\) = \(\frac{80}{9}\)