given two number is double the grater number and difference between smaller number and gcf 4 therefore smaller number is
Answers
Step-by-step explanation:
This question is based on the concept of PROPERTIES OF LCM AND HCF (OR GCF).
SO LET US START :-
THE QUESTION YOU MENTIONED ABOVE IS SOMEWHAT CONTAIN GLITCHES SO RIGHT QUESTION IS AS MENTIONED BELOW :-
LCM of two numbers is double than the greater number . And the difference between smaller number and GCF is 4 . Then the smallest number is ____.
LCM of two numbers is double than the greater number . And the difference between smaller number and GCF is 4 . Then the smallest number is ____.1) 8. 2)6. 3)12. 4)16.
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.