# Find the LCM and HCF of the following pair of integers and verify that LCM $\times$ HCF $=$ Product of two numbers:96 and 104.

Given :

The given numbers are 96, 104.

To find :

We have to find LCM and HCF of the given numbers and verify that $LCM \times HCF of the two numbers = Product of the two numbers$.

Solution :

Prime factorisation of $96 = 2\times 2\times 2 \times 2 \times2\times 3 = 2^5 \times 3^1$

Prime factorisation of $104 = 2\times 2\times 2 \times13 = 2^3 \times 13^1$

HCF $=$ Product of smaller power of each common prime factor.

HCF $= 2^3 = 8$.

LCM $=$ Product of highest power of each prime factor.

LCM $= 2^5\times 3^1\times 13^1$

$= 32 \times 3 \times 13$

LCM $= 1248$

Verification :

If x and y are two numbers,

$$HCF (x, y) \times LCM (x, y) = Product of the two numbers (x \times y)$$

$HCF (96, 104) \times LCM (96, 104) = 96 \times104$

$8 \times 1248 =96 \times104$

$9984 = 9984$

LHS = RHS .

Therefore, It is verified that $HCF (96, 104) \times LCM (96, 104) = 96 \times 104$

Updated on: 10-Oct-2022

27 Views 