Question

How we can find hcf and lcm from prime factorization?


plz tell me correct ans wer......​

Answer 1

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Prime factorisation method and division method are explained in Maths to determine the HCF(Highest Common Factor) and LCM(Least Common Multiple) of a number. Basically, we determine the prime factors of the given number such as 24, 12, 30, 100, etc. with this method. Here, we will learn to find the LCM and HCF of the numbers by both the methods.

Least Common Multiple

The least or smallest common multiple of any two or more given natural numbers are termed as LCM. It is also termed as Lowest Common Multiple.

For example, LCM of 10, 15, and 20 is 60.

Highest Common Factor

The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers. It is also known as GCD (Greatest Common Divisor).

For example, HCF of 4, 6 and 8 is 2.

Determination of LCM and HCF

We can find HCF and LCM of given natural numbers by two methods i.e. by prime factorization method or alternatively by division method. In the prime factorization method, given numbers are written as the product of prime* factors. While in the division method, given numbers are divided by the least common factor and continue still remainder is zero.

*(Prime numbers are numbers which have only two factors i.e. one and the number itself)

LCM By Prime Factorization method: Here given natural numbers are written as the product of prime factors. The lowest common multiple will be the product of the all prime factors with the highest degree (power)

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Answer 2

Correction:

How can we find HCF and LCM of numbers from their prime factorization?

Answer:

HCF of the numbers would be the common multiple of all the numbers with their lowest power given.

LCM of the numbers is the product of all the numbers in the factorization with their highest powers given

Let us understand through an example,

Take the numbers 12,60 and 36.

Prime factorization of the numbers:

12=2²×3

36=2²×3²

60=2²×3×5

HCF:

Recall the definitions again

Here,2 and 3 are common factors in all three numbers and take them with their lowest power.

So,

HCF=2²×3=4×3=12

And,

LCM:

Take all the numbers in the factorization with their greatest powers

LCM=2²×3²×5=4×9×5=180

-EXPLAINED