What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?
What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?
1012
1022
1122
1222
Solution
LCM of 3, 4, 5, 6 is 60. The number is of the form $60k + 2$. For the least four-digit value, $60k + 2 \ge 1000$ gives $k \ge 16.63$, so $k = 17$, giving $60 \times 17 + 2 = 1020 + 2 = 1022$.