( CNN) The leaders of the US and South Korea share a common goal: Get North Korea to abandon the nuclear and rocket programs that have rapidly expanded under the country’s supreme leader, Kim Jong Un.

But Chairwoman Moon Jae-in and Donald Trump, who gratified for the first time Thursday, have different ideas about how to get there.

Moon, a liberal who took office last month after his conservative predecessor was impeached on dishonesty charges, is a strong supporter of participation with Pyongyang.

How much injury can North Korea’s weapons do?

Foreign policy of South Korea from 1998 to 2008

Policy of involvement with North Korea on economic and political issues

Two South Korean Chairwomen traveled to Pyongyang

Earned South Korean President Kim Dae-jung a Nobel Peace Prize

Fewer North Korean nuclear and rocket exams during this period

Ultimately failed to stop North Korean nuclear program

Balancing act for new South Korean president