1 gallon white vinegar
1 cup salt
1 tablespoon dishwashing liquid

Mix well. Spray on a sunny day.

Or, just pour some boiling water (with or without salt) on paths to kill weeds between cobblestones, etc.

Some people dont like putting salt in their garden, but its a fun way to get rid of slugs/snails.

we lay newspaper and mulch our paths with hay/straw, you can use wood shavings or sawdust, or small stones. the sawdust will help stop the slug's n snails from crawling from bed to bed.

len

Here is a link that might be useful: len's garden page

Short of digging out the taproot, a teapot full of boiling water is my usual way.

Boiling water works pretty well for this but established perennial weeds will often return quickly. Using dishwashing liquid in the garden is not an organic practice; it's synthetically produced and is not on the OMRI list.

Vinegar, boiling water, salt, etc. will all kill this growth, for a time and will also allow some organic matter (those dead plants) to accumulate which when combined with the dust from the air will form a good soil for other plants to grow in.
The best way to clean weeds growing between pavers is to lift the pavers up and clean out the plants and any accululated soil that is there, a bit more physical labor but a longer term solution to the problem, unless the pavers are cemented in place.