If L.C.M and H.C.F of two numbers are 640 and 16 respectively, then ho

1.	If L.C.M and H.C.F of two numbers are 640 and 16 respectively, then how many such pairs are possible?1. 12. 23. 34. None of these
Answer» Correct Answer - Option 2 : 2 Given: L.C.M of two numbers = 640 H.C.F of two numbers = 16 Concept used: If H.C.F of two natural numbers is H, then numbers should be Hx and Hy respectively, where x and y should be relatively prime number. Formula used: The Product of H.C.F and L.C.M of any two numbers is equal to the product of that numbers. Calculation: Let, numbers be 16x and 16y respectively. Using formula, ⇒ 16x × 16y = 16 × 640 ⇒ x × y = 640/16 = 40 ⇒ x × y = 40 Possibilities of x, y = (1, 40), (2, 20), (4, 10), (5, 8) Here, only (1, 40) and (5, 8) are such pairs of relatively prime numbers. ∴ Only two pairs are possible.

If L.C.M and H.C.F of two numbers are 640 and 16 respectively, then how many such pairs are possible?1. 12. 23. 34. None of these

Answer» Correct Answer - Option 2 : 2

Given:

L.C.M of two numbers = 640

H.C.F of two numbers = 16

Concept used:

If H.C.F of two natural numbers is H, then numbers should be Hx and Hy respectively, where x and y should be relatively prime number.

Formula used:

The Product of H.C.F and L.C.M of any two numbers is equal to the product of that numbers.

Calculation:

Let, numbers be 16x and 16y respectively.

Using formula,

⇒ 16x × 16y = 16 × 640

⇒ x × y = 640/16 = 40

⇒ x × y = 40

Possibilities of x, y = (1, 40), (2, 20), (4, 10), (5, 8)

Here, only (1, 40) and (5, 8) are such pairs of relatively prime numbers.

∴ Only two pairs are possible.

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