Before you consider republishing your article on other platforms, it's important to focus on improving or rewriting weak content. To speed up the process for Google to index your articles, share them on Google+ as soon as you publish them on your website. You can then republish them on LinkedIn.
Rather than linking to your blog posts from LinkedIn, consider writing more articles than posts. This will make it easier for people to find your body of work without leaving the platform. Copy and paste the content of the article from your website into the LinkedIn article, and end it with a link to the original. You can also buy ready-made articles for sale from websites like Copiency.com.
This will generate more traffic to your website. After publishing the article, write a post to share it with your network. The published article will appear on your LinkedIn profile, giving you more exposure if you get a lot of profile views. Bookmark your own version of this page to quickly return to your list of items and statistics.
From time to time, write a post (status update) to point to one of your published articles. If your main site works with WordPress, you can link it to your Medium account. This will automatically republish any blog post you publish to your site on Medium. Copy and paste the content of your site into a new Medium story, modify the title, and include a call to action directing readers to the original article on your website.
Once published, other Medium users will be able to discover your content. If Google attributes those sites, not only will that item rank higher than yours, but your website will also be marked as having duplicate content. To avoid this, use the next line of code so that the site where your article is republished tells Google to give it full credit and not index the article on the external website.
Writing for medium publications is generally not compensated directly, except for revenue raised by pieces measured through the medium partner program. If you're worried that your site will be penalized for duplicate content, you can rewrite the article or develop a content strategy that's specific to LinkedIn and Medium.