Sanae Takaichi has been elected Japan's prime minister by parliament, making her the first woman to hold the office.

The 64-year-old won a clear majority on Tuesday - 237 votes in the powerful Lower House and another 125 in the Upper House - as leader of the ruling Liberal Democratic Party (LDP).

A staunch conservative and admirer of the late former British PM Margaret Thatcher, Takaichi takes over at a challenging economic moment as Japan grapples with rising costs of living and a frustrated public.

It's also been an uncertain time for the world's fourth-largest economy. She is the fourth PM in just five years, after her predecessors' terms were cut short by plunging ratings and scandals.

Although she defeated four men to win the LDP race in early October, her path to the top job appeared to be blocked when the LDP's long-time coalition partner, the Komeito party, withdrew support. But a last-minute deal with another opposition party - the right-leaning Japan Innovation Party (JIP), known as Ishin - saved her. She and the LDP will face voters next in 2028.

Meanwhile, Takaichi faces tricky relationships abroad. South Korea, which had started to mend historically delicate ties with Japan, is wary because of her right-wing politics, which lean nationalist. Like some of her predecessors, including the late former PM Shinzo Abe, she is seen as hawkish when it comes to an increasingly powerful China.

However, the most significant relationship is with the US, and Takaichi has a test coming soon - a meeting with US President Donald Trump next week. While both sides have reached a tariff deal, Trump's past comments questioning the value of a security treaty and demanding Tokyo pay more for defense have raised concerns.

At the age of 64, Takaichi is no stranger to Japanese politics. Known for her admiration of Thatcher, she is recognized for conservative views, including her opposition to same-sex marriage. Her recent campaign proposed expanded hospital services for women's health.

Takaichi still has a significant task ahead of her - to rebuild public trust in the LDP. The party has governed Japan for most of the past seven decades, but under previous leadership, it has faced major electoral defeats fueled by scandals. The LDP hopes that Takaichi's leadership will win back conservative voters disillusioned with their options.

In conclusion, while Takaichi's election marks a historic milestone for women in Japan, her conservative positions may challenge the expectations of progress laid out by her supporters.