Question

1 14. The H.C.F. and L.C.M. of two numbers is 128 and 14976 respectively. If one of the
number
is 1152, find the other number​

Answer 1

$\textsf{\underline{\underline{Answer :-}}}$

The second number is 1664

$\textsf{\underline{\underline{Explanation :-}}}$

Given :

HCF = 128

LCM = 14976

One Number = 1152

To Find :

The other number

Solution :

Consider the second number as x

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

$\sf{\implies} \: 128 \times 14976 = 1152 \times x$

$\sf{\implies} \: 1916928 = 1152x$

$\sf{\implies} \:x = \dfrac{1916928}{1152}$

$\sf{\implies} \:x = 1664$

$\therefore$ The second number is 1664

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Verification :-}}}$

$\sf{\implies} \: 128 \times 14976 = 1152 \times 1164$

$\sf{\implies} \: 1916928 =1916928$

$\therefore$ The second number is 1664

Answer 2

Explanation :-

Given :-

HCF of Two Number = 128

LCM of Two Numbers = 14979

One Number = 1152

To Find :-

Other Number

Formula Used :-

• LCM × HCF = Products of Two

Numbers

Solution :-

Let Other Number be x.

According To The Question,

LCM × HCF = Products of 2 Numbers

→ 128 × 14979 = 1152 × x

→ 1916928 = 1152x

→ 1916928 / 1152 = x

→ 1664 = x

.°. Other Number = 1664

_______________________________