Question

The LCM of the two positive integers is twice the largest number. the difference of the smaller number and the HCF of the two numbers is 4. the smaller number is

Answer 1

Answer:

The smallest number is 8

Step-by-step explanation:

Formula used:

Product of two numbers = Product of their L.C.M and G.C.M

Let the two integers be x and y with x > y.

As per given data,

L.C.M = 2x

y - G.C.D = 4

Also,

L.C.M * G.C.D = xyL.C.M∗G.C.D=xy (using formula)

(2x)* (y-4) = xy(2x)∗(y−4)=xy

2xy-8x= xy2xy−8x=xy

2xy-xy= 8x2xy−xy=8x

xy= 8xxy=8x

y= 8y=8

The smallest number is 8