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Find HCF and LCM of 404 and 96 and verify that HCF$×$LCM $ =$ Product of the two given numbers.
Given: Number 404 and 96.
To do: To Find HCF and LCM of 404 and 96 and verify that HCF$\times$LCM $=$ Product of the two given numbers.
Solution:
Using the factor tree for the prime factorization of
404 and 96, we have,
$404=2^{2}\times101$ and $96=2^{2}\times6$
To find the HCF, we list common prime factors and their smallest exponent in 404 and 96
As under :
Common prime factor $=2$, Least exponent$=2$
$\therefore$ HCF$=2^{2}=4$
To find the LCM,
we list all prime factors of 404 and 96 and their greatest exponent as follows:
Prime Factor of 404 and 96 | Greatest Exponent |
2 | 5 |
3 | 1 |
101 | 1 |
$\therefore$ LCM$=2^{5}\times3^{1}\times101^{1}=9696$
HCF$\times$ LCM $= 9696\times4 = 38784$
Product of two numbers $= 404\times96 = 38784$
Therefore HCF $\times$ LCM $=$ Product of two numbers.
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