Question

Find the smallest number which when divided by 5,8,12,15&20 leaves the same remainder 3.

Answer 1

take LCM of all the numbers:
$5 - 3 = 2 = 1 \times2\\ 8 - 3 = 5 = 1 \times 5 \\ 12 - 3 = 9 = 3 \times 3$
$15 - 3 = 12= 2 \times 2 \times 3\\ 20 - 3 = 17 = 1 \times 17\\ lcm = 2 \times 2 \times 3 \times 3 \times 5 \times 17$
LCM is 3060.
question says smallest number,so that number would be 3063.

Answer 2

5 × 8× 12 × 15× 20 + 3 = 14403