Question

The smallest number which when divided by 4, 6, or 7 leaves a remainder of 2 is

• A. 44
• B. 62
• C. 80
• D. 86

Hint:

Subtract the remainder from the number and take the LCM of divisors.

Answer 1

The Correct Option is D

We are looking for the smallest number \( N \) such that: \[ N \equiv 2 \pmod{4}, \quad N \equiv 2 \pmod{6}, \quad N \equiv 2 \pmod{7} \] This implies: \[ N - 2 \equiv 0 \pmod{\text{lcm}(4,6,7)} N - 2 \equiv 0 \pmod{84} N = 84 + 2 = \boxed{86} \]