Question

find hcf and lcm of 404 and 96 and verify that hcf×lcm =product of two numbers (fully solved please)

Answer 1

Solution :-

HCF of 404 and 96

404 = 2*2*101

96 = 2*2*2*2*2*3

Common Factors = 2*2 

HCF of 404 and 96 = 4

LCM of 404 and 96

404 = 2*2*101

96 = 2*2*2*2*2*3

LCM = 2*2*2*2*2*3*101 = 9696

LCM of 404 and 96 is 9696

HCF × LCM = Product of the two numbers 

⇒ 4*9696 = 404*96

⇒ 38784 = 38784

LHS = RHS

Hence, it is verified.

Answer 2

Solution :

Resolving the given Numbers

into prime factors , we get

404 = 2 × 2 × 101 = 2² × 101

96 = 2×2×2×2×2×3 = 2^5×3

HCF(404,96) = 2² = 4

[ Product of the smallest power

of each common prime factors

of the numbers ]

LCM( 404,96) = 2^5 × 101 × 3

= 9696

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We know that ,

If h, l are HCF and LCM of

two numbers a and b then

l × h = a × b

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Verification :

l = 9696 ,

h = 4 ,

a = 404 ,

b = 96

l × h = 9696 × 4 = 38784 --(1)

a × b = 404 × 96 = 38784---(2)

Therefore ,

From (1) and (2) , we conclude

that

l × h = a × b

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