Question

) Find HCF of 370 and 592 by prime factorization method. Hence find
their LCM.

Answer 1

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Answer 2

Concept:

In mathematics, Least Common Multiple is referred to LCM by its entire name, whereas Highest Common Factor is its complete name. The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the H.C.F. describes the biggest factor existing between any given pair of two or more numbers. LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).

We have two key techniques—the division method and the prime factorization approach—for determining H.C.F. and L.C.M.

Multiplication of two numbers = HCF x LCM

Given:

370 and 592

Find:

Find HCF of 370 and 592 by prime factorization method. Hence find

their LCM.

Solution:

Using prime factorisation,

370= 2 x 5 x 37

592= 2⁴ x 37

HCF= 2 x 37

      =74

we know,

Multiplication of two numbers = HCF x LCM

⇒370 x 592 =74 x LCM

⇒LCM = 370 x 592 /74

            =460

Therefore, HCF =74 and LCM =460

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