Question

On dividing a certain number by 8, 10, 12, 14 the remainder is always 3. Which is the smallest such number?

Answer 1

2	8	10	12	14
2	4	5	6	7
	2	5	3	7

Let us find the LCM of the given divisors.
LCM = 2 × 2 × 2 × 5 × 3 × 7 = 840.
To the LCM we add the remainder obtained every time.
Hence, that number = LCM + remainder = 840 + 3 = 843