Question

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

Answer 1

To Find :

• we need to find the HCF and LCM

Given :

• LCM is 12 times the HCF
• product of two numbers is 3072

we know that,

• HCF × LCM = product of two numbers.

Let HCF be x , then LCM is 12x

Now ,

⟹ HCF × LCM = product of two numbers.

⟹ x × 12x = 3072

⟹ 12x² = 3072

⟹ x² = 3072/12

⟹ x² = 256

⟹ x = √256

⟹ x = 16

So,

• LCM of two numbers (x) = 16
• HCF of two numbers 12x = 12 × 16 = 192

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

• LCM of number is 12 times their HCF

• The product of the numbers is 3072

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The value of HCF and LCM

${\green{\underline{\underline{\bold{Solution:-}}}}}$

According to 1st condition:-

Let the HCF of the numbers be x

Then LCM = 12x

As we know that

The product of numbers = Product of LCM and HCF

Given:- Product of numbers = 3072

Therefore:-

$\implies \sf3072 = HCF \times LCM$

$\implies \sf3072 = (x)\times (12x)$

$\implies \sf3072 =12 {x}^{2}$

$\implies \sf \dfrac{3072}{12} = {x}^{2}$

$\implies \sf 256 = {x}^{2}$

$\implies \sf x = \sqrt{256}$

$\implies \sf x = 16$

Therefore:-

HCF = x = 16

LCM = 12x = 16 × 12 = 192

Hence:-

$\large \boxed{\sf \pink{ \rightarrow HCF = 16}}$

$\large \boxed{\sf \purple{ \rightarrow LCM = 192}}$