Question

The HCF of two numbers is 16 and the LCM is 96. If one of the numbers is 32. what
is the other number?​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Second Number is 48.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

The HCF of 2 number = 16

LCM = 96

One Number = 32

To Find :

The Second Number

Solution :

Consider the number as x

$\boxed{\sf{HCF \times LCM = Product\:of\:2\:numbers}}$

$\tt{\implies} \:16 \times 96 = 32 \times x$

$\tt{\implies} \:1536 = 32x$

$\tt{\implies} \:x = \dfrac{1536}{32}$

$\tt{\implies} \:x = 48$

$\therefore$ The Second Number is 48.

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\tt{\implies} \:16 \times 96 = 32 \times 48$

$\tt{\implies} \:1536 = 1536$

$\therefore$ The Second Number is 48.

Answer 2

☞ HCF of two numbers is 16 and LCM is 96.

• HCF = 16

• LCM = 96

Product of two numbers = LCM × HCF

=> 96 × 16

• Also it is said that one number is 32.

Let another number be M.

Then;

=> M × 32 = 16 × 96

=> M = $\dfrac{16\:\times\:96}{32}$

=> M = $\dfrac{1536}{32}$

=> M = 48

______________________________

Other number = M = 48

_____________ [ANSWER]

✡ Product of two numbers = LCM × HCF

The two numbers are : 32 and 48

LCM = 96 and HCF = 16

=> 32 × 48 = 96 × 16

=> 1536 = 1536

____________ [HENCE VERIFIED]