Question

If HCF of two number is 1/6 of there LCM and one number twice the HCF of the number find the second number when sum of this number is 120​

Answer 1

Answer:

48 and 72

Step-by-step explanation:

Let H be the HCF and L be the LCM of 2 numbers x and y.

Also, H * L = x * y   ⇒ y = (H * L) / x   ...(i)

According to the question,

H = (1/6) L

⇒6H = L   ...(ii)

x = 2H   ...(iii)

x + y = 120   ...(iv)

Using (i) in (iv)

x +  (H * L) / x = 120

x + (H * 6H) / x = 120   ∵ L = 2H

2H + ( 6H²) / 2H = 120   ∵ x = 2H

2H + 3H = 120

5H = 120

H = 120 / 5

H = 24

L = 6H = 6 * 24 = 144

x = 2H = 2 * 24 = 48  ⇒ x = 48

x + y = 120

48 + y = 120

y = 120 - 48

y = 72

∴ The 2 numbers are 48 and 72.