# Find the LCM and HCF of the following pair of integers and verify that $LCM \times HCF =$ Product of two numbers : 36 and 64.

Given :

The given numbers are 36, 64.

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 $36 = 2\times 2\times 3 \times 3 = 2^2 \times 3^2$

Prime factorisation of $64 = 2\times 2\times 2\times 2\times 2\times2 = 2^6$

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

HCF $= 2^2 = 4$.

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

LCM $= 2^6\times 3^2$

$= 64 \times 9$

LCM $= 576$

Verification :

If x and y are two numbers,

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

$HCF (36, 64) \times LCM (36, 64) = 36 \times 64$

$4 \times 576=36 \times 64$

$2304 = 2304$

LHS $=$ RHS .

Therefore, It is verified that $HCF (36, 64) \times LCM (36, 64) = 36 \times 64$

Updated on: 10-Oct-2022

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