Question

WHAT IS THE RELATION BETWEEN LCM AND HCF​

Answer 1

Answer:

H.C.F x L.C.M = product of the numbers

Step-by-step explanation:

Answer 2

The relation between LCM and HCF is as follows:

(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

(ii) The LCM of given co-prime numbers is equal to the product of the numbers since the HCF of co-prime numbers is 1.

So, LCM of Co-prime Numbers = Product Of The Numbers

Example 2: 17 and 23 are two co-prime numbers. By using the given numbers verify that,

LCM of given co-prime Numbers = Product of the given Numbers

Solution: LCM and HCF of 17 and 23:

17 = 1 x 7

23 = 1 x 23

LCM of 17 and 23 = 391

HCF of 17 and 23 = 1

Product of 17 and 23 = 17 × 23 = 391

Hence, LCM of co-prime numbers = Product of the numbers

(iii) H.C.F. and L.C.M. of Fractions

LCM of fractions = LCM of Numerators / HCF of Denominators

HCF of fractions = HCF of Numerators / LCM of Denominators

Example 3: Find the LCM of the fractions 1 / 2 , 3 / 8, 3 / 4

Solution:

LCM of fractions = LCM of Numerators/HCF of Denominators

LCM of fractions = LCM (1,3,3)/HCF(2,8,4)=3/2

Example 4: Find the HCF of the fractions 3 / 5, 6 / 11, 9 / 20

HCF of fractions HCF of Numerators/LCM of Denominators

HCF of fractions = HCF (3,6,9)/LCM (5,11,20)=3/220

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