Question

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

Answer 1

Given: `8/9, 10/27` and `16/81`

Step-wise calculation:

1. Use the rules for fractions:

HCF of fractions = `"HCF (numerators)"/"LCM (denominators)"`

LCM of fractions = `"LCM (numerators)"/"HCF (denominators)"`

2. Prime-factorise:

Numerators: 8 = 2³

10 = 2 × 5

16 = 2⁴

HCF (numerators) = `2^min(3, 1, 4) = 2` 

LCM (numerators) = `2^max(3, 1,4) xx 5` 

= 2⁴ × 5

= 16 × 5

= 80

Denominators: 9 = 3²

27 = 3³

81 = 3⁴ 

HCF(denominators) = `3^min(2, 3, 4)`

= 3²

= 9 

LCM(denominators) = `3^max(2, 3, 4)`

= 3⁴

= 81

3. Apply the formulas:

HCF = `"HCF (numerators)"/"LCM (denominators)"`

= `2/81`

LCM = `"LCM (numerators)"/"HCF (denominators)"`

= `80/9`

HCF `(8/9, 10/27, 16/81) = 2/81`

LCM `(8/9, 10/27, 16/81) = 80/9`