Question

l.s.a of two positive numbers a large number than that is the difference between a small number. and their g.s.a. 4, a small number? answer the question in English ​

Answer 1

Answer:

THIS QUESTION IS BASED ON THE CONCEPT OF PROPERTIES OF HCF AND LCM.

SOLUTION :- LET US TAKE TWO NUMBERS :-

SAY "a" and "b". AND THERE IS ONE CONDITION ALSO "a<b".

So, LCM(a,b) = 2b (ACCORDING TO QUESTION). ••••••••• (1)

a - GCF (a,b) = 4 (ACCORDING TO QUESTION). ••••••••••• (2)

So From Equation (2) , we get

a - 4 = GCF (a,b) [BY APPLICATION OF LINEAR EQUATION] •••••••••• (3).

SO BOTH THE EQUATIONS (1) & (3) LOOK LIKE THIS :-

LCM (a,b) = 2b ••••••••••• (1)

GCF (a,b) = a - 4 ••••••••••• (3)

SO BY MULTIPLYING (1) & (3) , WE GET ,

LCM (a,b) × GCF (a,b) = [a-4] [2b]

a × b = [a-4] [2b] (♤♡◇ Because LCM (a,b) × GCF (a,b) = a × b ♤♡◇)

a × b = [a-4] [2b]

ab = [a-4] [2b]

ab / 2b = a - 4. (BY APPLICATION OF LINEAR EQUATION)

a / 2 = a - 4. (ab / 2b = a / 2)

a / 2 + 4 = a (BY APPLICATION OF LINEAR EQUATION)

a + 8 / 2 = a. (BY TAKING LCM (2,1) = 2)

a + 8 = 2 × a. (BY APPLICATION OF LINEAR EQUATION)

a + 8 = 2a

8 = 2a - a (BY APPLICATION OF LINEAR EQUATION)

8 = a

HENCE a IS SMALLER NUMBER SO WE GET 8 AS ITS ANSWER.

ANS :- SO YOUR FINAL ANSWER IS 8.

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