Question

Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF =

product of two numbers



18 and 120.​

Answer 1

Answer:

$\red\bigstar$ LCM of 18 and 120 = 360.

$\blue\bigstar$ HCF 18 and 120 = 6.

SOLUTION

 LCM  

To find the LCM of 18 and 120, first we must do the prime factorization of 18 and 120 .

18 = 2 × 3 × 3

120 = 2 × 2 × 2 × 3 × 5

∴ The LCM of 18 and 120 =  2 × 2 × 2 × 3 × 3 × 5

The LCM of 18 and 120 = 360.

 HCF  

To find the LCM of 18 and 120, first we must do the prime factorization of 18 and 120 .

18 = 2 × 3 × 3

120 = 2 × 2 × 2 × 3 × 5

∴ The HCF of 18 and 120 = 2 × 3 = 6

VERIFICATION

We have to verify that LCM x HCF = Product of two numbers

RHS

Product of Two Numbers = 18 × 120

Product of Two Numbers = 2160

LHS

LCM x HCF = 6 × 360

LCM x HCF = 2160

Here LHS = RHS , Hence Verified.