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Relation( L. C. M., H. C. F. )#4 Important Topic By Lalit Sir 2021

HCF and  LCM Relation

The followings are the relation between HCF and LCM. Go through the relation between HCF and LCM, solve the problem using the relations in an easy way.

(i) The product of LCM and HCF of the given natural numbers is equivalent to the product of the given numbers.

From the given property, LCM × HCF of a number = Product of the Numbers

Consider two numbers A and B, then.

Therefore,LCM (A , B) × HCF (A , B) = A × B

Example 1: Show that the LCM (6, 15) × HCF (6, 15) = Product(6, 15)

Solution: LCM and HCF of 6 and 15:

6 = 2 × 3

15 = 3 x 5

LCM of 6 and 15 = 30

HCF of 6 and 15 = 3

LCM (6, 15) × HCF (6, 15) = 30 × 3 = 90

Product of 6 and 15 = 6 × 15 = 90

Hence, LCM (6, 15) × HCF (6, 15)=Product(6, 15) = 90

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