Question

If the hcf of two numbers is 24 and lcm is 1344 difference between the number is 80 what is sum of the number

Answer 1

AnswEr:-

Sum of two numbers = 368

Step-by-step-explanation:-

Let the two numbers be M & N respectively.

☯First case:-

• LCM = 1344
• HCF = 24

We know,

$\star\:\large{\boxed{\mathfrak\blue{LCM \times HCF = Product \: of \: numbers }}}$

• Putting values:-

⇒ 1344 × 24 = M × N

⇒ MN = 32256 ...............(Eq.1)

☯2nd case:-

• Difference between the numbers = 80

⇒ M - N = 80

⇒ (M - N)² = (80)²

[Identity:- (a - b)² = (a + b)² - 4ab]

⇒ (M + N)² - 4MN = 6400

⇒ (M + N)² - 4 × 32256 = 6400

⇒ (M + N)² = 6400 + 129024

⇒ (M + N)² = 135424

⇒ M + N = √135424

⇒ M + N = 368

$\therefore{\underline{\textsf{Sum \: of \: numbers = {\textbf{368 }}}}}$

Answer 2

Answer:

• HCF of Numbers = 24
• LCM of Numbers = 1344
• Difference b/w Numbers = 80

Let the Numbers be a and, b.

☢ We Know that :

↠ HCF × LCM = Product of Number

↠ 24 × 1344 = a × b

↠ ab = 32,256

____________________

☢ Difference between Number :

⇴ (a – b) = 80

• Squaring Both Sides

⇴ (a – b)² = (80)²

• (a – b)² = (a + b)² – 4ab

⇴ (a + b)² – 4ab = 6400

⇴ (a + b)² = 6400 + 4(32,256)

⇴ (a + b)² = 6400 + 129,024

⇴ (a + b)² = 135,424

• Squaring Root Both Sides

⇴ (a + b) = 368

∴ Sum of the Numbers will be 368.