Question

the product of two numbers is 25920, if the lcm of the two numbers is 720 find their HCF

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given :

The product of two numbers is 25920.

LCM of two numbers is 720.

To Find :

HCF (highest common factor )

We know that Product of two numbers say 'a' and 'b' is equal to the product of its LCM and HCF

$\bold{\boxed{a \times b = HCF\times LCM}}$

$25920 =HCF\times 720$

$\sf HCF= \dfrac{25920}{720} = \dfrac{2592}{72} = \dfrac{1296}{36} = \dfrac{648}{18}$

$= > \dfrac{648}{18} = \dfrac{324}{9} = 36$

$\therefore$ HCF of two numbers is 36.

It means the two numbers having 36 as a highest common factor.

Extra information=>

LCM of two numbers is 720 and HCF is 36

720 can be written as $\bold{36\times 20}$

HCF is 36

Now,$\bold{[36\times 20][36]}$

$\bold{[36\times 10\times2][36]}$

$\bold{[36\times 10][36\times2]}$

$\therefore$The numbers are 360,72

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given :

The product of two numbers is 25920.

LCM of two numbers is 720.

To Find :

HCF (highest common factor )

We know that Product of two numbers say 'a' and 'b' is equal to the product of its LCM and HCF

$\bold{\boxed{a \times b = HCF\times LCM}}$

$25920 =HCF\times 720$

$\sf HCF= \dfrac{25920}{720} = \dfrac{2592}{72} = \dfrac{1296}{36} = \dfrac{648}{18}$

$= > \dfrac{648}{18} = \dfrac{324}{9} = 36$

$\therefore$ HCF of two numbers is 36.

It means the two numbers having 36 as a highest common factor.

Extra information=>

LCM of two numbers is 720 and HCF is 36

720 can be written as $\bold{36\times 20}$

HCF is 36

Now,$\bold{[36\times 20][36]}$

$\bold{[36\times 10\times2][36]}$

$\bold{[36\times 10][36\times2]}$

$\therefore$The numbers are 360,72