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 …………
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Step-by-step explanation:
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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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