Question

LCM of number is 12 times their HCF . the product of the numbers is 3072. then find their HCF and LCM​

Answer 1

Answer:

Let HCF= x

Therfore, LCM = 10x

As we know,

LCM × HCF = Product of two numbers

x × 10x = 3072

10x² = 3072

x² = 3072/10

x = 17.52

Now,

HCF = x = 17.52

LCM = 10x = 175.2

Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• LCM is 12 times the HCF

• Product of two numbers is 3072

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• HCF and LCM

Formula to be used :-

• HCF × LCM = product of two numbers.

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Let HCF be x.

Given that,

LCM is 12 times the HCF

Then LCM will be = 12x

Again, it’s given that

Product of two numbers is 3072.

_____________________________________________________

According to the question :-

⟼ HCF × LCM = product of two numbers.

⟼ x × 12x = 3072

⟼ 12x² = 3072

⟼ x² = 256

⟼ x = √256

⟼ x = 16

Hence,

LCM of two numbers = 16

HCF of two numbers = 12x = 12 × 16 = 192