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:

8 is the correct answer

Answer 2

Given:  

Two numbers = x and y and x > y

LCM = 2x

GCF = y - 4

To Find:

The smallest number

Solution:

LCM × GCF = Product of the numbers

LCM × GCF = x × y

2x × ( y -4 ) = xy

2xy - 8x - xy = 0

xy - 8x = 0

x ( y - 8) = 0

x = 0 and y = 8

Now, the value of x can not be zero, thus -

HCF = y - 4

= 8 - 4 = 4

Answer: The smallest number is (A) 8.