Question

8. The product of two numbers is 1,029. Find the HCF of the numbers if their
LCM is 147.
Two containers have 27 litres and 36 litres of milk. What is the capacity​

Answer 1

${\huge {\underline {\sf {Correct\:Question}}}}$

The product of two numbers is 1,029. Find the HCF of the numbers if their LCM is 147.

${\underline{\underline {\sf {Given:}}}}$

• Product of two number is 1029.
• The LCM of the numbers = 147

${\underline {\underline {\sf {Find:}}}}$

• The HCF of the numbers.

${\underline {\underline{\sf {Solution:}}}}$

• We know that, product of two numbers = HCF × LCM
• Now, as we have the product that is 1029 and the LCM that is 147

Let the HCF of the given numbers be x,

$\implies}$ Product of two numbers = HCF × LCM

$\implies}$Now substituting the values in equation :

$\implies}$ ${\rm {1029\: =\: x \:×\: 147}}$

$\implies{\rm {x\:=\:\dfrac {1029 }{147}}}}$

$\implies}$ ${\rm {x\: =\:7}}$

Therefore, the HCF of the two numbers is 7.

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$\huge\drag$Verification :

• Product of two numbers = HCF × LCM

Putting values in formula ,

$\implies}$ ${\rm {1029\: =\: 7\:×\: 147}}$

$\implies}$ ${\rm {1029\: =\: 1029}}$

LHS = RHS

Hence, it is verified.

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