Angular update from 8 to 13 peer dependency problem

I had the exact same problem today. This is how I fixed it:

npx @angular/cli@11 update @angular/core@11 @angular/cli@11 --force
# now getting the same errors as above
npm install @angular-devkit/build-angular@~0.1102.18 --force
git checkout -- .
npx @angular/cli@11 update @angular/core@11 @angular/cli@11 --force

Now go to package.json and remove the line containing @angular-devkit/build-ng-packagr.

Execute this lines:

rm package-lock.json
rm -rf node_modules
npm install

Done!

Maybe removing that particular line from package.json plus npm install would have been enough and the other commands above where unnecessary but I rather tell you all I did :)

By the way before I tried all this I also downgraded to npm v7 as suggested in one of the comments above but I don't think this was necessary or did any help.

I just had this exact problem, and running this command did it for me:

npm install @angular-devkit/build-angular@~0.1102.18 --force