I have been reading about the STR & my first problem came very much in the beginning. So, as per the simplest form of the Lorentz transforms, we have

$$x' = (x - vt)\gamma \tag{1.1}$$

$$t' = (t - vx/c^2)\gamma \tag{1.2}$$

$$\gamma = \frac{1}{\sqrt{1- v^2/c^2}} \tag{1.3}$$

And this makes sense. However, then it proceeds to the length contraction & time dilation part. Where we get that

$$L = \gamma L' \tag{2.1}$$

$$T = T'/\gamma \tag{2.2}$$

I don't understand this. This seems to have a conflict with Lorentz transforms we stated above. Since in both of those transforms, the gamma was the denominator. Also, this relationship between length & time implies that they're inversely proportional, since L*T cancels out the gamma, as opposed to the regular relationship between the space & time which is directly proportional. One more thing I find odd is that,

$$x' = ct' \tag{3}$$

Satisfies the speed of light in vaccuo constraint & so does the

$$x = ct \tag{4}$$

However, while, if we say that

$$c = L'/T' \tag{5.1}$$

$$c \ne L/T \tag{5.2}$$

Since,

$L/T = L'/(T'\gamma^2) \tag{6}$

$L/T$ will only be equal to $L'/T'$ if $v=0$ or very insignificant. But in that case, this function collapses to the simple Galleili transforms since the frame $K'$ would no longer be considered a moving frame but rather just a stationary frame shifted slightly at the x axis.

Where am I getting it wrong? Because, to me, the formulas presented for time dilation & length contraction seem in direct conflict with one another & also, if considered together seem in conflict with Lorentz transforms & speed of light in vaccuo.