Looking on the internet deeply has found these results:

become prime minister with the election is the most popular phrase on the web.

become prime minister by the election 154,600,000 results on the web	become prime minister with the election 161,400,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
He wishes to follow Richelieu and become prime minister. Churchill would become Prime Minister, that would lead to a bolder approach to Germany! If we win this vote, there'll be a general election and Margaret will become Prime Minister. Patrice Lumumba, becomes Prime Minister, after years of Belgium colonial power. A letter from the prime minister by special courier. You don't get to be Prime Minister by accident. The duty falls upon me as your Sovereign to invite you to become Prime Minister... and to form a government in my name. That Sophia plans to cancel once she becomes Prime Minister.	Churchill would become Prime Minister, that would lead to a bolder approach to Germany! He wishes to follow Richelieu and become prime minister. If we win this vote, there'll be a general election and Margaret will become Prime Minister. I mean, you're elected as Prime Minister with a brief to bat for Britain. In the meantime, a Class The duty falls upon me as your Sovereign to invite you to become Prime Minister... and to form a government in my name. Patrice Lumumba, becomes Prime Minister, after years of Belgium colonial power. That Sophia plans to cancel once she becomes Prime Minister.

become prime minister by the election

154,600,000 results on the web

become prime minister with the election

161,400,000 results on the web

More popular!

He wishes to follow Richelieu and become prime minister.
Churchill would become Prime Minister, that would lead to a bolder approach to Germany!
If we win this vote, there'll be a general election and Margaret will become Prime Minister.
Patrice Lumumba, becomes Prime Minister, after years of Belgium colonial power.
A letter from the prime minister by special courier.
You don't get to be Prime Minister by accident.
The duty falls upon me as your Sovereign to invite you to become Prime Minister... and to form a government in my name.
That Sophia plans to cancel once she becomes Prime Minister.

Churchill would become Prime Minister, that would lead to a bolder approach to Germany!
He wishes to follow Richelieu and become prime minister.
If we win this vote, there'll be a general election and Margaret will become Prime Minister.
I mean, you're elected as Prime Minister with a brief to bat for Britain.
In the meantime, a Class
The duty falls upon me as your Sovereign to invite you to become Prime Minister... and to form a government in my name.
Patrice Lumumba, becomes Prime Minister, after years of Belgium colonial power.
That Sophia plans to cancel once she becomes Prime Minister.