Question

Using prime factorisation, fi nd the HCF and LCM of:
(i) 8, 9, 25 (ii) 12, 15, 21 (iii) 17, 23, 29
(iv) 24, 36, 40 (v) 30, 72, 432 (vi) 21, 28, 36, 45​

Answer 1

Step-by-step explanation:

I) 8= 2³×1

9= 3²×1

25=5²×1

HCF= product of common terms with the highest power.

= 1

LCM= product of prime factors with highest power

= 2³×3²×5²= 8×9×25= 1800

ii) 12= 2²×3

15= 3×5

21= 3×7

HCF= 3

LCM= 2²×3×5×7= 420

iii) 17, 23, 19

Remember: HCF of prime numbers is 1 and LCM of prime numbers is the product of numbers.

HCF= 1

LCM= 17×23×19

= 11339

Iv) 24, 36, 40

24= 2³×3

36= 2²×3²

40= 2³×5

HCF= 2²= 4

LCM= 2³×3²×5= 360

v) 30= 2×3×5

72= 2³×3²

432= 2⁴×3³

HCF= 2×3= 6

LCM= 2⁴×3³×5= 16×27×5= 2160

vi) 21=3×7

28= 2²×7

36= 2²×3²

HCF= 1

LCM= 3²×2²×7= 252

I hope it will help you...