Consider those numbers between 300 and 400 such that when each number is divided by 6, 9 and 12, it leaves 4 as remainder in each case. What is the sum of the numbers?
Solution
LCM of 6, 9, 12 = 36
The required number are $4 + 36 \times n$
where $n = 1, 2, 3$ and Numbers are between 300 and 400.
so, possible values of $n$ are 9 and 10.
The numbers are $4 + 36 \times 9 = 328$
$4 + 36 \times 100 = 364$
sum = 692