The ratio of the difference to L.C.M of two natural numbers is 4 : 21.

1.	The ratio of the difference to L.C.M of two natural numbers is 4 : 21. If their H.C.F is 6, find the smaller number.1. 182. 123. 64. 42
Answer» Correct Answer - Option 1 : 18 Given: Ratio of difference to L.C.M of two natural numbers = 4 : 21 H.C.F of two natural numbers = 6 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. Calculation: H.C.F of two numbers = 6 Let, numbers = 6x and 6y (x, y are relatively prime number) L.C.M of 6x and 6y = 6xy Difference of numbers = 6x – 6y (let, 6x 6y) ⇒ (6x – 6y)/6xy = 4/21 (Given) ⇒ (x – y)/xy = 4/21 ⇒ 21(x – y) = 4xy ⇒ x = 7, y = 3 (7 and 3 are relatively prime number) Numbers = 6 × 7 = 42 and 6 × 3 = 18 ∴ The smaller number = 18

The ratio of the difference to L.C.M of two natural numbers is 4 : 21. If their H.C.F is 6, find the smaller number.1. 182. 123. 64. 42

Answer» Correct Answer - Option 1 : 18

Given:

Ratio of difference to L.C.M of two natural numbers = 4 : 21

H.C.F of two natural numbers = 6

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.

Calculation:

H.C.F of two numbers = 6

Let, numbers = 6x and 6y (x, y are relatively prime number)

L.C.M of 6x and 6y = 6xy

Difference of numbers = 6x – 6y (let, 6x 6y)

⇒ (6x – 6y)/6xy = 4/21 (Given)

⇒ (x – y)/xy = 4/21

⇒ 21(x – y) = 4xy

⇒ x = 7, y = 3 (7 and 3 are relatively prime number)

Numbers = 6 × 7 = 42 and 6 × 3 = 18

∴ The smaller number = 18

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