Apple has agreed to purchase streaming music service LaLa, according to multiple reports. LaLa fills a big hole in Apple’s digital music strategy and could bring streaming down music from cloud into iTunes-ready devices everywhere. LaLa has technology that copies users’ iTunes music collections into cloud servers, so that users can play back songs on internet-connected devices. This feature would ease an Apple transition from locally-stored to cloud-based music. That’s attractive to Apple because iPhone and iPod Touch use flash memory, which’s limited in its capacity compared to hard drives in earlier iPods. In addition, that scarce memory gets shared with video, photos, apps and data associated with apps, whereas hard drives in iPods were used mostly or even exclusively for music. And as a bonus, Lala can play last few hundred songs from a cache when there’s no internet connection which lets it play cloud-based music in subways, highways and remote locations.