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Trying to merge these three objects so these three lines will disappear. How to achieve this?

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You have placed separate boxes side by side. You have no tools in the free version of SketchUP to join them so that there's no seams. Paid version has boolean operators which do this and thus make the paid version much more easy to use. You must extrude a shape as one if you want it to be one.

You can obviously disable edge stroke display. That makes exactly fitting separate parts to look out seamless.

Your problem seems to be more severe. The parts are not fitting or they are misplaced. I bet your smallest part has wrong rotational position. SketchUP is poor if you try to assemble separately made pieces. It's very easy to leave small gaps as you have done. Especially rotations are difficult. You should make the parts in-place to make them fit. More developed programs allow gap filling for non-fitting parts and assembling fitting separate parts exactly, no matter should some of them be rotated. Easy to use freeware hasn't such functions.

Check DesignSpark Mechanical - it's a free 3D modeller with ultra-easy user interface and some tools which are missing from the free version of SketchUP. It outputs files which are readable and usable in SketchUP.

Hopefully the next image shows what I mean by writing "make parts in-place". The screenshot series is from DesignSpark Mechanical:

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The parts are merged in this case automatically as they are drawn. But Merging is not obligatory, it can be disabled to keep some parts separate.

Disabling stroke display:

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In the left all surface pieces have strokes. In the middle only separate parts have edge strokes. In the right there's no strokes.

One really wants to keep parts separate when they are separate in reality. Separate parts can easily be moved apart to show also hidden details:

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    Thanks a lot for help. Very well explained. So to start learning 3D modelling, you think it's good to use DesignSpark Mechanical? What about AutoCAD or any other? Thank you. – Ramona Jan 6 at 18:58
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    @Ramona AutoCAD and its clones are the inherited load from the past. They do their job, but the user interface is much more intuitive in modern programs. I bet you cannot shell out $2000,- so start with freeware. D.S.Mechanical is a decimated version of SpaceClaim and that's something of today. You maybe can get Autodesk Fusion 360 for free, if you are not a business user. Check it, too. Full Fusion 360 for free is not at all a bad option. Check more options from here: all3dp.com/1/best-free-cad-software-2d-3d-cad-programs-design – user287001 Jan 6 at 19:33
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    @Ramona I must add one freeware: PTC Creo Elements. It also has a free version, which still seems impressive altough it's heavily decimated from the paid version. I havent run it because it tries to make some own permanent internet connection which my system denies. – user287001 Jan 6 at 22:53
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    You should also consider OnShape - also free - wicked powerful, decent learning curve. onshape.com – GerardFalla Jan 7 at 17:14
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    @GerardFalla will check this one, too. Thank you very much. – Ramona Jan 9 at 16:44

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