# State Fundamental theorem of arithmetic. Is it possible for the HCF and LCM of two numbers to be 18 and 378 respectively. Justify your answer.

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State Fundamental theorem of arithmetic. Is it possible for the HCF and LCM of two numbers to be 18 and 378 respectively. Justify your answer.

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Solution: Every composite number can be expressed (factorised) as a product of primes and this factorisation is unique, apart from the order in which the prime factors occur. Yes.

Justification: HCF of two numbers is always a factor of their LCM. But here 18 is a factor of 378.

Hence, Two numbers can have 18 as their HCF and 380 as their LCM.