Why were Sherman Grant and Lee all headed toward Richmond at the end of war?

At the end of the Civil War, Union General Ulysses S. Grant and Confederate General Robert E. Lee were both heading toward Richmond, Virginia, as the city was the Confederate capital and a key strategic location. Grant aimed to encircle and defeat Lee's Army of Northern Virginia, effectively ending the war. Meanwhile, Lee was attempting to regroup his forces and escape to consolidate with other Confederate troops. The eventual confrontation led to Lee's surrender at Appomattox Court House, marking a significant turning point in the war.