Let's roll up our sleeves and solve this. We have 603 and we're going to multiply it by 23, essentially adding 603 to itself 23 times.
Step 1: 0 + 603 = 603
Step 2: 603 + 603 = 1206
Step 3: 1206 + 603 = 1809
Step 4: 1809 + 603 = 2412
Step 5: 2412 + 603 = 3015
Step 6: 3015 + 603 = 3618
Step 7: 3618 + 603 = 4221
Step 8: 4221 + 603 = 4824
Step 9: 4824 + 603 = 5427
Step 10: 5427 + 603 = 6030
Step 11: 6030 + 603 = 6633
Step 12: 6633 + 603 = 7236
Step 13: 7236 + 603 = 7839
Step 14: 7839 + 603 = 8442
Step 15: 8442 + 603 = 9045
Step 16: 9045 + 603 = 9648
Step 17: 9648 + 603 = 10251
Step 18: 10251 + 603 = 10854
Step 19: 10854 + 603 = 11457
Step 20: 11457 + 603 = 12060
Step 21: 12060 + 603 = 12663
Step 22: 12663 + 603 = 13266
Step 23: 13266 + 603 = 13869

So, 603*23 = 13869