The least number, which when divided by 4, 5 and 6 leaves remainder 1, 2 and 3 respectively, is

When a number is divided by P, Q or R leaving remainders X, Y or Z respectively such that the difference between divisor and remainder in each case is same i.e., (P – X) = (Q – Y) = (R – Z) = T (say) then that (least) number must be in the form of (K – T), where K is LCM of P, Q and R Here 4 – 1 = 3, 5 – 2 = 3, 6 – 3 = 3 ∴ The required number = LCM of (4, 5, 6) – 3 = 60 – 3 = 57