Good question and one you need to answer, carefully. The single most common beginner's mistake is to use too much magnification. Magnification has much less to do with astronomy than beginners think. Astronomy is more about seeing faint objects, not about magnifying them and seeing faint objects is more about telescope aperture, in terms of mirror or objective size, rather than magnification.
Going overboard on magnification not only destroys image quality, it also makes your astronomy telescope much harder to use. A rule of thumb for all optical devices is that as magnification goes up, image quality, image brightness, field of view and image steadiness all go down. If you are experiencing poor image quality with your telescope, if objects are too hard to find (narrow field of view), or if the telescope shakes and vibrates too much, your magnification is likely too high. This is especially serious when it comes to the many faint objects we want to see, since we lose image brightness quickly as magnification goes up. Less magnification is more for much of astronomy.
"Maximum useable magnification" listings by manufacturers are basically advertising nonsense. Ignore them. The amount of magnification you use will depend on a variety of factors - the type of object being observed, observing conditions of the atmosphere (very important), the size and quality of your scope, your observing experience as well as your personal preferences.
There is no magic formula for determining maximum magnification for your optical telescope, but the oft quoted rule of thumb of 30-50x per inch of telescope sizes as a maximum is a good place to start. Why 30-50x, instead of just 50x? The atmosphere is a significant factor in determining how much magnification you can use on a given night and conditions change, nightly, and even by the hour. On nights when the atmosphere is turbulent, you will be down around the 30x or less per inch of telescope if you want good image quality. On nights of exceptional steadiness, you may be able to use 50x per inch of telescope size. Keep in mind, though, that the atmosphere and mount problems limit magnification to 300x or a bit more for any telescope, no matter how large, and even, then, that much will be used only, rarely. Most of the time you will use much, much less.
Using this guideline, we can see that 120x is a real stretch for a 60mm (2.4") scope. You can certainly get more magnification out of a 60mm telescope by changing eyepieces or using a barlow, but images will be blurry and indistinct. This is an example of nonsense magnification and it is often advertised on cheap telescopes as a sales pitch. When we pass the point where adding more magnification gives us less detail, not more, we know we are using too much magnification. Using these same guidelines we can also see that the same 120x is hardly a challenge for even a 127mm (5") telescope. If you want to see more, use a larger telescope, not more magnification.