Question

0.2. 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

Step-by-step explanation:

✤ Required Answer:

✒ GiveN:

LCM is double the greater number.

Difference between GCD and smaller number is 4.

✒ To FinD:

Find the smaller number

✤ How to Solve?

For solving this question, we need to know a simple relation between LCM, GCD and the numbers.

LCM is the lowest common multiple of the numbers and GCD/HCF is the highest common factor of the two numbers.

➤ Important conditions

So, By using this concepts, Let's solve the question.

✤ Solution:

Let the numbers be a and b

Here consider a is greater number and b is smaller number. That is a > b

We have,

LCM = 2(Greater number)

HCF = Smaller number - 4

That is,

➙ LCM = 2a

➙ GCD = b - 4

We know,

LCM × HCF = product of numbers,

Then,

➙ 2a × (b - 4) = ab

➙ 2ab - 8a = ab

➙ 2ab - ab = 8a

➙ ab = 8a

➙ ab - 8a = 0

➙ a(b - 8) = 0

So,

b = 8

Because, Greater number can't be 0, So, b = 8. Smaller number among the two 8

pls mark as the brainliest it would be a pleasure!!