Question

hcf of two numbers is 24 and their lcm is 1344.if difference between numbers is 24

Answer 1

Your answer lies in the attachment.

Some necessary info :-

Notice in Fig.1, we've got two values of y, but we chose only one. Why ??

Just because, we need to choose a positive number. Although it's not mentioned here in the question, we always need to consider the numbers as positive. Thus, only the positive value of y ,i.e., 168, is applicable here.

Answer :- 168 and 192

Answer 2

$\mathfrak{\huge{Hi!}}$

$\sf{Let\:the\:numbers\:be = a, b}$

Then :

HCF(a,b) = 24

LCM(a,b) = 1,344

Difference = a - b = 24

=》 a = 24 + b ...(1)

We know that :-

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

=》 $\tt{24 \times 1,344 = ab}$ ...(2)

Put (1) in (2) :

=》 $\tt{32,256 = (24 + b)b}$

=》 $\tt{b^{2} + 24b - 32,256}$

=》 $\tt{b = 168, (-384)}$ ( by further solving, you will get this answer )

=》 b = 168 ( since the number can't be negative )

a = 24 + b

a = 192

$\boxed{\sf{a = 192 , b = 168}}$