To divide 62124 by 3 using the boxes and dots method, we can represent 62124 as boxes filled with dots, where each box represents a place value.
6 | 2 | 1 | 2 | 4
\bullet \bullet \bullet \bullet \bullet \bullet | \bullet \bullet | \bullet | \bullet | \bullet \bullet \bullet
Now, we need to distribute the dots equally among 3 groups.
Starting from the leftmost box:
- In the first box, we have 6 dots, so we can put 2 dots in each group.
- In the second box, we have 2 dots, so we can put 0 dots in each group and carry over 2 dots to the next box.
- In the third box, we have 1 dot from the carry-over, so we have a total of 1 + 1 = 2 dots. We can put 1 dot in each group and carry over 1 dot.
- In the fourth box, we have 2 dots from the carry-over, so we have a total of 2 + 2 = 4 dots. We can put 1 dot in each group and carry over 1 dot.
- In the last box, we have 4 dots from the carry-over, so we have a total of 4 + 4 = 8 dots. We can put 2 dots in each group and there is no carry-over.
Therefore, 62124 ÷ 3 = 20708.
\boxed{20708}