Well, let's see... finding the least residue of a number modulo another number involves finding the remainder when we divide the original number by the modulo.
For 1789 (mod 4), we divide 1789 by 4 and get a remainder of 1. So the least residue is 1, which means that 1789 is congruent to 1 modulo 4.
Now, for 1789 (mod 10), we divide 1789 by 10 and again get a remainder of 9. So the least residue is 9, which means that 1789 is congruent to 9 modulo 10.
Lastly, for 1789 (mod 101), we divide 1789 by 101 and get a remainder of 86. So the least residue is 86, which means that 1789 is congruent to 86 modulo 101.
And there you have it! The least residues of 1789 modulo 4, 10, and 101 are 1, 9, and 86 respectively.