N is the least six-digit number which, when divided by 4, 5, 6, 10 and 15, leaves a remainder of 3 in each case. What is the sum of the digits of N?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6
A number leaving the same remainder 3 with each divisor is 3 more than a multiple of their LCM. The least six-digit one is found from the first multiple of the LCM at or above 100000.
LCM of 4, 5, 6, 10, 15 \(=2^{2}\times3\times5=60\)
\(100000\div60\) leaves remainder 40, so \(100000-40=99960\) is a multiple of 60
Next multiple: \(99960+60=100020\)
\(99960+3=99963\) has only five digits, so \(N=100020+3=100023\)
Sum of digits \(=1+0+0+0+2+3=6\)
The sum of the digits of N is 6.