Question

Find the smallest number which leaves 22, 35, 48 and 61 as remainders when divided by 26, 39, 52 and 65 respectively.

A) 242
B) 462
C) 682
D) 902

Answer 1

The smallest number that satisfies all the given conditions is 682

Step-by-step explanation:

To find the smallest number that leaves given remainders when divided by different numbers, we can use the concept of the Chinese Remainder Theorem. We need to solve a system of congruences to find the solution.

Using the given remainders and divisors, we have:

1. x ≡ 22 (mod 26)
2. x ≡ 35 (mod 39)
3. x ≡ 48 (mod 52)
4. x ≡ 61 (mod 65)

By solving this system of congruences, the smallest number that satisfies all the conditions is 682 (Option C).