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"shared a common understanding" is correct and usable in written English.
You can use it when two people or groups have some kind of mutual agreement or understanding about something. For example: "The two sides of the debate shared a common understanding that the proposal would be beneficial to all."
Exact(4)
President Rousseff's office said Brazil and the European Union shared a "common understanding" on data privacy.
Lenders and debtors shared a common understanding: In spite of strained debtor-country budgets, all renegotiated external indebtedness would be treated equally in priority of payment.
Prime Minister Yoshihiko Noda kept up the pressure, telling the same committee he believed the Bank of Japan shared a common understanding with the government on the need to beat deflation.
Yet we shared a common understanding: that climate change is real, that it poses a major threat to our future, and that Congress must stop denying the science and start acknowledging the need for action.
Similar(56)
It is only when Russia and Europe share a common understanding of past events that something durable can be built between them.
Ninety-five per cent of the scholars considered various protections for the freedom of speech as essential, yet just sixty-seven per cent thought that, in principle, it was necessary for political leaders across the parties "to generally share a common understanding of relevant facts".
All these models share a common understanding that innovation activities can broadly be described and visualized in process models.
A key factor for integration is that tools share a common understanding regarding the meaning of the exchanged terms and services.
Participatory modelling must often deal with the challenge of ambiguity when diverse stakeholders do not share a common understanding of the problem and measures for its solution.
We share a common understanding that the capacity and extent of human impact on earth ecosystems have changed profoundly, human induced climate change has already brought about notable adverse repercussions on society and economic development.
Project alignment is the process of ensuring that key stakeholders share a common understanding of the project mission, goals, objectives, tactics, work processes and plans and have the required competences and skills.
Related(20)
shared a common view
shared a mutual understanding
shared a common interpretation
represented a common understanding
sharing a common understanding
shared a profound understanding
shared a common stair
shared a common design
shared a common commitment
shared a common enemy
shared a common hatred
shared a common trait
shared a common vision
shared a common cause
shared a common currency
shared a common passion
shared a common interest
shared a common complaint
shared a common ancestry
shared a common answer
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com