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:

LCM = 2⁴ × 3 × 7 = 3024.

HCF = 2 × 3 = 6.

the number product is 18,144

the product of LCM and HCF is18,144

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

$\red\bigstar \rm \blue{ The \: HCF \: of \: 336 \: and \: 54 \:  = 6}</p><h2><u>L.C.M.</u></h2><p>For also finding the LCM of 336 and 54 , let us first do the prime factorization of 336 and 54</p><p>✩ 336 = 2 × 2 × 2 × 2 × 3 × 7</p><p>✩ 54 = 2 × 3 × 3 × 3</p><p>∴ The LCM of 336 and 54 = 2 × 3 × 2 × 2 × 2 × 7 × 3 × 3</p><p>[tex] \red\bigstar \rm \blue{The \: LCM \: of \: 336 \: and \: 54  = 3024}$

$\bigstar \rm \purple{Verification }$

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.