Question

the lcm of two positive integers is twice the larger number. the difference of the smaller number and the hcf of the two number is 4. find the smaller number.

Answer 1

Answer:

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

Step-by-step explanation:

please mark brainliest

Answer 2

$Let \: the \: number \: be \: x \: H \: and \: y H \: where \: H \: is \: the \:$

$\\ HCF \: and \: yH > x \: H$

$\\ ∴LCM = xy \: H$

$\\ ∴xy H = 2y H⇒x = 2$

$\\ Again,x \: H - H = 4$

$\\ ⇒2H - H = 4⇒H = 4$

$\\ ∴Smaller \: number \: = pH = 2 \times 4 = 8$

I hope this will help you dear..

Always stay safe and stay healthy..