A number when divided successively by 6, 7 and 8, it leaves the respective remainders of 3, 5 and 4, what will be the last remainder when such a least possible number is divided successively by 8, 7 and 6 ?

Working backwards from the successive divisions: if a number leaves remainder 4 when divided by 8, that quotient leaves remainder 5 when divided by 7, and that quotient leaves remainder 3 when divided by 6, the least such number is 201. When 201 is divided successively by 8, 7, 6: 201 ÷ 8 = 25 remainder 1, 25 ÷ 7 = 3 remainder 4, 3 ÷ 6 = 0 remainder 3. The final remainder is 3.