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