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Question

Using prime factorization, find the HCF and LCM of $$ { \text { } 36,84 } .  $$ 
Also verify that: HCF $$\times \mathrm { LCM } =$$ product of given numbers.


Solution

Prime factor of given no.s

$$36=2\times 2\times 3\times 3\\$$
$$84=2\times 2\times 3\times 7\\$$
$$LCM=2\times 2\times 3\times 3\times 7=252\\$$
$$HCF=2\times 2\times 3=12\\$$
$$LCM\times HCF=1524\\$$
$$Product =36\times 48=1524$$

Hence proved.
$$HCF ×LCM=$$ product of given numbers.

Maths

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