Question

Find the HCF and LCM of 18 and 24 using prime factorisation . Verify that HCF × LCM = a×b​

Answer 1

HCF 6

LCM 72

Step-by-step explanation:

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Answer 2

Given:

Two numbers a = 18 and b = 24

To be found:

The HCF and the LCM of the two numbers And verify HCF × LCM = a×b​ (Product of two numbers)

So,

By prime factorization,

18 = 2 × 3 × 3 = 2 × 3²

And

24 = 2 × 2 × 2 × 3 = 2³ × 3

So,

HCF(18,24) = 2 × 3 = 6

[Hint - see the common numbers and take the lowest power]

Now,

LCM(18,24) = 2³ × 3² = 72

[Hint - Take common numbers with their highest power and also write the numbers that are left.]

Now,

Verification:-

HCF × LCM = Product of two numbers

LHS = 6 × 72 = 432

And

RHS = 18 × 24 = 432

Hence,

LHS = RHS (verified)

$\star$ Important Note-

'HCF × LCM = Product of two numbers' can only be done when there are two numbers. It is not applicable in the situation of more than two numbers.