i. HCF = 12, LCM = 252

Prime factorization of given numbers -

36 = 2 × 2 × 3 × 3

84 = 2 × 2 × 3 × 7

So HCF = product of common factors = 2 × 2 × 3 = 12

And LCM = product of prime factors with highest powers = 2² × 3² × 7 = 252

Verification -

HCF × LCM = product of numbers

⇒ LHS = 12 × 252 = 3024

⇒ RHS = 36 × 84 = 3024

∵ LHS = RHS(Hence verified)

ii. HCF = 1, LCM = 713

Prime factorization of given numbers -

23 = 23 × 1

31 = 31 × 1

So HCF = product of common factors = 1

And LCM = product of prime factors with highest powers = 23 × 31 = 713

Verification -

HCF × LCM = product of numbers

⇒ LHS = 1 × 713 = 713

⇒ RHS = 23 × 31 = 713

∵ LHS = RHS(Hence verified)

iii. HCF = 4, LCM = 9696

Prime factorization of given numbers -

96 = 2 × 2 × 2 × 2 × 2 × 3

404 = 2 × 2 × 101

So HCF = product of common factors = 2 × 2 = 4

And LCM = product of prime factors with highest powers = 2⁵ × 3 × 101 = 9696.

Verification -

HCF × LCM = product of numbers

⇒ LHS = 4 × 9696 = 38784

⇒ RHS = 96 × 404 = 38784

∵ LHS = RHS(Hence verified)

iv. HCF = 18, LCM = 1584

Prime factorization of given numbers -

144 = 2 × 2 × 2 × 2 × 3 × 3

198 = 2 × 3 × 3 × 11

So HCF = product of common factors = 2 × 3 × 3 = 18

And LCM = product of prime factors with highest powers = 2⁴ × 3² × 11 = 1584

Verification -

HCF × LCM = product of numbers

⇒ LHS = 18 × 1584 = 28512

⇒ RHS = 144 × 198 = 28512

∵ LHS = RHS(Hence verified)

v. HCF = 36, LCM = 11880

Prime factorization of given numbers -

396 = 2 × 2 × 3 × 3 × 11

1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5

So HCF = product of common factors = 2 × 2 × 3 × 3 = 36

And LCM = product of prime factors with highest powers = 2³ × 3³ × 5 × 11 = 11880

Verification -

HCF × LCM = product of numbers

⇒ LHS = 36 × 11880 = 427680

⇒ RHS = 396 × 1080 = 427680

∵ LHS = RHS(Hence verified)

vi. HCF = 128, LCM = 14976

Prime factorization of given numbers -

1152 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

1664 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 13

So HCF = product of common factors = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128

And LCM = product of prime factors with highest powers = 2⁷ × 3² × 13 = 14976

Verification -

HCF × LCM = product of numbers

⇒ LHS = 128 × 14976 = 1916928

⇒ RHS = 1152 × 1664 = 1916928

∵ LHS = RHS(Hence verified)