How to properly update child dependencies in package.json and package-lock.json?

Question

Node.js

Suppose I have two independent parent packages, each with a different version of the child dependency in the package.json file.

During installation, the latest version of child is installed in the node_modules folder, as a result, the first parent starts to fail due to a mismatch between the versions of the installed child.

How to find which version of child will be compatible with both parent and where to register it?