Question

Find the LCM and HCF of the following pairs of integers and verify that LCM× HCF = product of the two numbers.
336 and 54​

Answer 1

Answer:

Answer

Prime factorisation of 336=2×2×2×2×3×7

Prime factorisation of 54=2×3×3×3

Hence, LCM of 336,54=2×3×2×2×2×7×3×3=3024

And HCF of 336,54=2×3=6

Now, LCM × HCF =3024×6=18144

Also, 336×54=18144

i.e., HCF × LCM = Product of the two numbers

Answer 2

 ✳ SOLUTION ✳  

⋆HCF⋆

For Finding HCF of 336 and 54 , let us first do the prime factorization of 336 and 54

♢ 336 = 2 × 2 × 2 × 2 × 3 ×7

♢ 54 = 2 × 3 × 3 × 3

∴ The HCF of 336 and 54 = 2 × 3

$\blue\bigstar$ The HCF of 336 and 54  = 6

✳LCM✳

For also finding the LCM of 336 and 54 , let us first do the prime factorization of 336 and 54

✩ 336 = 2 × 2 × 2 × 2 × 3 × 7

✩ 54 = 2 × 3 × 3 × 3

∴ The LCM of 336 and 54 = 2 × 3 × 2 × 2 × 2 × 7 × 3 × 3

$\red\bigstar$ The LCM of 336 and 54  = 3024

Verification

We have to verify that :-  LCM× HCF = product of the two numbers.

⋆LCM = 3024

⋆HCF = 6

⋆The Two numbers are 336 and 54

LHS

HCF × LCM = 6 × 3024

HCF × LCM = 18144

RHS

Product of the two numbers = 336 × 54

Product of the two numbers = 18144

$\boxed {\boxed{\boxed{\sf LHS = RHS }}}$

∴ Verified that LCM× HCF = Product of the two numbers