Because that is the easiest way to calculate the LCM for 2 "random" numbers. Assuming you know the prime factorization of each term (which could be hard)

@Calvin Lin
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ok you are saying that its easiest way so what about 4 we can also use this in factorization i know its not a prime number but y cant we use this i didnt got the answer of my question yet

The "HCF" is the "Highest Common Factor" of a given list of integers. The highest common factor is the integer which can divide each and every integer in the given list.

The "LCM" is the "Lowest Common Multiple" of a given list of integers. The lowest common multiple is the smallest integer which is divisible by each and every integer in the given list.

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TopNewestCheck out the wikis of Lowest Common Multiple and Greatest Common Divisor.

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please tell the reason of prime factorization why do we just take prime factors for lcm

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Because that is the easiest way to calculate the LCM for 2 "random" numbers. Assuming you know the prime factorization of each term (which could be hard)

Do you know the proof of the following theorem?

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okay so whats the application of this lcm and hcf???

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The "HCF" is the "Highest Common Factor" of a given list of integers. The highest common factor is the integer which can divide each and every integer in the given list.

The "LCM" is the "Lowest Common Multiple" of a given list of integers. The lowest common multiple is the smallest integer which is divisible by each and every integer in the given list.

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what about its applications

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