What is the least number which, when divided by 60, 84, and 96, leaves remainders of 28, 52, and 64, respectively?

Let's assume the least number is 'y' which, when divided by 60, 84, and 96, leaves remainders of 28, 52, and 64, respectively.

Here the difference between divisor and remainders is the same which is given below.

(60-28) = 32, (84-52) = 32, (96-64) = 32

So the required number = y = LCM of (60, 84, and 96) - 32

LCM of (60, 84, and 96) = $$2\times\ 2\times\ 2\times\ 2\times\ 2\times\ 3\times\ 5\times\ 7$$

= 3360

required number = y = 3360 - 32

= 3328