Broadcom’s final push to buy Qualcomm for $121 billion started Monday.

The Singapore chipmaker made a “best and final” offer of $82 a share — higher than its prior $70 proposal — and privately met Monday with leading Qualcomm shareholders in New York, sources said.

Qualcomm itself has not engaged with fellow smartphone chipmaker Broadcom in what would be the biggest technology deal ever.

A tie-up could be hindered by a culture clash, sources said.

Broadcom CEO Hock Tan is a cost-cutting private-equity-like investor, while Qualcomm is run by a bunch of freer-spending scientists, sources said.

Tan plans to spend the next few weeks traveling the US — from Boston to Chicago and Los Angeles — meeting with leading Qualcomm shareholders in a full-out proxy election campaign, sources said.

Broadcom expects to meet in mid-February with proxy advisory firm Institutional Shareholder Services (ISS) to win its support before Qualcomm’s March 6 annual meeting, sources said.

Several Top 20 Qualcomm shareholders had told Broadcom execs in recent weeks they would support a sale at more than $80 a share, a leading Qualcomm shareholder told The Post.

Broadcom declined comment.