Question

find hcf and lcm of 336 and 54? verify it?

Answer 1

$\huge\mathfrak\green{Answer:}$

Given:

We have been given two numbers 336 and 54.

To Find:

We neee to find their HCF and LCM.

Solution:

We can find the HCF of 336 and 54 by Euclid's Division algorithm.

Clearly 336>54,

So, we need to divide 336 by 54 until we don't get remainder as zero.

[Division shown in attachment]

On dividing 336 by 54, we have

336 = 54 × 6 + 12

54 = 12 × 4 + 6

12 = 6 × 2 + 0

Hence the HCF of 336 and 54 is 6.

Now, we can find their LCM by prime factorization method.

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

= 2^4 × 3 × 7

Prime factorization of 54 = 2 × 3 × 3 × 3 = 2 × 3^3

LCM = 2^4 × 3 × 7 = 3024

Verification:

We know that HCF × LCM = Product of numbers.

HCF × LCM = 6 × 3024 = 18144

Product of numbers = 336 × 54 = 18144

Hence HCF × LCM = product of numbers.

Hence verified!!