Question 11
The smallest number of 4-digits leaving a remainder of 1 when divided by 2 or 3 or 4 or 6 has
Solution
A number leaving remainder 1 on division by 2, 3, 4, 5 and 6 is of the form $$60k + 1$$, because the LCM of these divisors is 60. The smallest 4-digit number of this form is $$60 \times 17 + 1 = 1021$$. Its digits are 1, 0, 2 and 1, so it contains only one zero.
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