equation simplification. $(5y-1)/3 + 4 =(-8y+4)/6$ Simplification of this equation gives two answers when approched by two different methods.
Method 1 Using L.C.M( least common multiple)
$(5y-1)/3 + 4 =(-8y+4)/6$
$(5y-1+12)/3 = (-8y+4)/6$
$5y-11 =  (-8y+4)/2$
$(5y-11)2= (-8y+4)$
$10y-22 = -8y+4$
$18y=26$
$y = 26/18=13/9$
Method 2 multiplying every term by 3
$3(5y-1)/3 + 4*3 = 3(-8y+4)/6$
$5y-1 + 12 = (-8y+4)/2$
$2(5y-1 + 12) = -8y+4$
$10y-2+24  =  -8y+4$
$18y + 22 = 4$
$18y = -18$
$y = -1$
The correct method is method 2 and the correct answer is y = -1
Why is method 1 is incorrect? Could anyone explain why the answer is wrong when using the L.C.M( method 1)?

They are both correct methods. (Actually they are so similar they really can't really be considered to be different methods.)
It's just that you did the second without making an arithmetical error, and you did the first with an arithmetical error.
$5y - 1 + 12 = 5y +11 \ne 5y-11$.
Fix that and every thing will work out fine.
