Question

find the hcf of 256 and 36 also find their lcm and verify that lcm ×hcf= product of two numbers​

Answer 1

Step-by-step explanation:

(i) HCF of 256 and 36:

Prime factorization of 256 = 2⁸

Prime factorization of 36 = 2² * 3²

HCF(256,36) = 4

(ii) LCM of 256 and 36:

Prime factorization of 256 = 2⁸

Prime factorization of 36 = 2² * 3²

LCM(256,36) = 2⁸ * 3²

                      = 2304.

Verification:

Product of LCM * HCF = 9216

Product of two numbers = 9216.

∴ LCM * HCF = Product of two numbers.

Hope it helps!

Answer 2

Answer: 9216

Step-by-step explanation:

HCF of 256 and 36

Prime factorization of 256

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2⁸

Prime factorization of 36

= 2 × 2 × 3 × 3

= 2² × 3²

Therefore

HCF(256,36) = 4

LCM of 256 and 36

Prime factorization of 256

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2⁸

Prime factorization of 36

= 2 × 2 × 3 × 3

= 2² × 3²

LCM(256,36)

⇒ 2⁸ × 3² = 2304.

Verify :-

LCM × HCF = Product of two numbers

LCM × HCF = 9216

Hence Verified