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 …………​

Answer 1

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Step-by-step explanation:

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Answer 2

Answer:

The required smaller number is 8

Step-by-step explanation:

Let a and b be the numbers with a>b

Then by the given condition

LCM = 2a

Now

b - GCF = 4

⇒ GCF = b-4

Again

LCM x GCF = a x b

LCM x GCF = a x b⇒ 2a x (b-4) = a x b

LCM x GCF = a x b⇒ 2a x (b-4) = a x b⇒ 2a(b- 4) - ab = 0

LCM x GCF = a x b⇒ 2a x (b-4) = a x b⇒ 2a(b- 4) - ab = 0⇒ a [2(b-4) - b] = 0

⇒ 2(b-4)-b = 0 [ since a # 0]

⇒ 2b - 8 - b = 0

⇒ 2b - 8 - b = 0⇒ b = 8

So the required smaller number is 8

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