Question

L.C.M. of the given two numbers is double the greater number. And the difference between smaller number and G.C.F. is 4. Therefore the smaller number is ………… (A) 8 (B) 6 (C) 12 (D) 16

Answer 1

Answer:

A) 8

Step-by-step explanation:

Let a and b, a>b be the two numbers

GIVEN

• LCM = 2a

• b - GCF = 4 ⇒ GCF = b-4

CALCULATION

We know that

LCM x GCF = a x b

⇒ 2a x (b-4) = a x b

⇒ 2a x (b- 4) - ab = 0

⇒ a x [2(b-4) - b] = 0

Since a cannot be zero

⇒ 2(b-4)-b = 0

⇒ 2b - 8 - b = 0

⇒ b = 8

Answer 2

Answer:

(a) = 8

Step-by-step explanation:

Given that L.C.M of the given two no is double the greater number.

Let the no. be x and y

According to the question

L.C.M = 2x

y - G.C.F = 4

G.C.F = ( y - 4 )

Hence,

x × y = L.C.M. × G.C.F.

xy = 2x × ( y - 4 )

xy = 2xy - 8x

xy - 2xy = ( - 8x )

- xy = -8x

y = 8

Hence, the smaller no is 8.

Thanks!