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Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF $=$ Product of the integers:
404 and 96
Given:
Given pair of integers is 404 and 96.
To do:
Here we have to find the LCM and HCF of the given pair of integers and then verify that LCM $\times$ HCF $=$ Product of the integers.
Solution:
Calculating LCM and HCF using prime factorization method:
Writing the numbers as a product of their prime factors:
Prime factorisation of 404:
- $2\times2\times101=2^2\times101$
Prime factorisation of 96:
- $2\times2\times2\times2\times2\times3 =\ 2^5\ \times\ 3^1$
Multiplying the highest power of each prime number of these values together:
$2^5\ \times\ 3^1\ \times\ 101^1\ =\ 9696$
LCM(404, 96) $=$ 9696
Multiplying all common prime factors:
$2^2\ =\ 4$
HCF(404, 96) $=$ 4
Now, verifying that LCM $\times$ HCF $=$ Product of the integers:
LCM $\times$ HCF $=$ Product of the integers
404 $\times$ 96 $=$ 9696 $\times$ 4
38784 $=$ 38784.
Hence verified.
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