According to Sidney van den Bergh's The Galaxies of the Local Group
(2000), the LMC was a a quiescent galaxy with little star formation for billions of years. Then three billion years ago it started forming stars at an elevated rate, and about one billion years ago or less it was practically starbursting. It is still forming stars at a high rate.
There has been speculation that the Large and the Small Magellanic Clouds began interacting at some time in the past, and that this may have triggered increased star formation. My gut feeling, for what it is worth, suggests to me that the LMC and the SMC may have passed quite close to one another one billion years ago (or less), and that this may have coincided with and perhaps caused the most intense star formation in the LMC.
Even if we bear in mind that the Large and the Small Magellanic Clouds differ considerably not only in size but in mass, it is clear that the LMC is both yellower and more ultraviolet than the SMC. That is to say that the LMC has a well-defined yellow population (in its bar), wheras the SMC lacks an obvious and concentrated old population. But the LMC also has many more and larger emission nebulas and clusters of hot stars than the SMC.
This suggests to me that the LMC has more of a history as a galaxy than the SMC, but it also has larger reservoirs of gas. It could well be that it has stolen some of its present starforming material from the SMC. In fact, it seems to have stolen some of its stars from the SMC:
So they collided 300 million years ago? That is quite recently. And "collided" is a strong word. It seems to me that a true head-on collision with the SMC should have distorted the LMC so much that its bar should look less straight than it does today. Of course, we don't know what sort of collision it really was (assuming it happened at all), and I guess it is possible that the bar of the LMC could have survived unscathed, while its spiral arms (assuming it had any) could have been messed up. And the SMC in its present form could be a large, well-mixed and somewhat gas-deficient assembly of debris from from that collision.
But all things considered, I think that a real head-on collision as recently as 300 million years ago should have produced more present-day chaos and galactic upheaval than we see today.
In any case, there is definitely evidence of past interactions between the LMC and the SMC, however you look at it. In Sidney van den Bergh's book there is an illustration showing star clusters located between the LMC and the SMC, forming a sort of bridge between the two galaxies.
I have to wonder what will happen when (or if) our own Milky Way starts snaring the LMC in the same way that the LMC snared the SMC. Will the LMC sparkle even more with star formation when (or if) it is plunging helplessly toward the Milky Way, or will it turn on the lights in our own galaxy?