Question

# Find $$HCF$$ and $$LCM$$ of $$404$$ and $$96$$ and verify that $$HCF\times LCM=$$ product of the two given numbers.

Solution

## Let $$a=404$$ and $$b=96$$Expressing the number as a product of prime number$$404=2\times 2\times 101$$$$96=2\times 2\times 2\times 2\times 2\times 3$$$$\therefore$$ LCM of 404 and 96 is $$2\times 2\times 2\times 2\times 2\times 101\times 3=9696$$$$\therefore$$ HCF of 404 and 96 is $$2\times 2=4$$Now,  $$HCF\times LCM=4\times 9696=38784$$Product of two given numbers $$404\times 96=38784$$Hence $$HCM\times LCM=$$ Product of two given numbers.Maths

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