Question

D. The H.C.F. of two numbers is 11 and their L.C.M.
is 693. If one of the numbers is 77, then the other
number is .....
​

Answer 1

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

The second number is 99.

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

Given :

H.C.F of the 2 numbers = 11

L.C.M of the 2 numbers = 693

One number of them = 77

To find :

The second number

Solution :

LCM = 693

HCF = 11

One Number = 77

Second number = y

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

$\sf{\implies} \: 693 \times 11 = 77 \times y$

$\sf{\implies} \: 7623 = 77y$

$\sf{\implies} \: y = \dfrac{7623}{77}$

$\sf{\implies} \:y = 99$

$\therefore$ The second number is 99.

$\rule{300}{1}$

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

$\sf{\implies} \: 693 \times 11 = 77 \times 99$

$\sf{\implies} \: 7623 = 7623$

$\therefore$ The second number is 99.

Answer 2

Answer : 99

EXPLANATION :

Given,

HCF of two numbers = 11

LCM of those numbers = 693

One of the number = 77

Let the other number be x

HCF × LCM = Product of two Numbers

11 × 693 = 77 × x

x = 11 × 693 / 77

x = 11 × 9

x = 99

Therefore, the other number is 99.