Question

find the lcm and hcf of the following pairs of integers and verify that lcm x hcf = product of the two numbers 336 and 54​

Answer 1

Answer:

HCF=6

LCM=3024

Step-by-step explanation:

336= 2×2×2×2×3×7 = 2^4 ×3×7

54= 2×3×3×3 = 2× 3^3

HCF=2×3

=6

LCM=2^4 × 3^3 × 7

=3024

HCF×LCM= 6×3024

= 18144

Product of the number= 336×54

=18144

therefore.,

HCF×LCM=Product of the number

Hence verified...

Hope it is Helpful...:)

Answer 2

$\huge\fbox \red{Solution:}$

H.C.F.

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

$\red\bigstar \rm \blue{ The \: HCF \: of \: 336 \: and \: 54 \:  = 6}$

L.C.M.

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

$\red\bigstar \rm \blue{The \: LCM \: of \: 336 \: and\: 54  = 3024}$

$\bigstar \rm \purple{Verification }$

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

⋆LCM = 3024

⋆HCF = 6

⋆The Two numbers are 336 and 54

L.H.S

HCF × LCM = 6 × 3024

HCF × LCM = 18144

R.H.S

Product of the two numbers = 336 × 54

Product of the two numbers = 18144

$\fbox \blue{LHS=RHS}$

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