Question

If the HCF of 2 numbers is 23 and the LCM is 1449. One of the numbers is 161 . Find the other number with explanation.

Answer 1

Given

$\bold { HCF \ of \ two \ numbers} = 23\\\bold{ LCM \ of \ two \ numbers} = 1449$

One of the number = 161

Let the other number be x

SOMETHING YOU NEED TO KNOW

$\boxed{\bold{HCF * LCM = Product \ of \ the \ two \ numbers}}$

$\implies 23 * 1449 = 161 * x$

$\implies 33327 = 161 x$

$\implies x = \dfrac{33327}{161}$

$\implies x = 207$

VERIFY

Product of 161 and 207 = 161 * 207

                                        = 33327

Hence verified !

$\boxed{\boxed{\bold{Therefore\ the \ other \ number \ is \ 207}}}}$

                                                     

Answer 2

Step-by-step explanation:

Given -

HCF = 23

LCM = 1449

One of the number = 161

To Find -

The other number

Let x be the other number

Now,

As we know that :-

• LCM × HCF = Product of two numbers

It means,

» 1449 × 23 = 161 × x

» x = 1449 × 23/161

» x = 9 × 23

» x = 207

Hence,

The other number is 207

Verification -

• LCM × HCF = Product of two numbers

» 1449 × 23 = 207 × 161

» 33,327 = 33,327

LHS = RHS

Hence,

Verified..