Question

Find the least possible number which when divided by 36, 49, 54 or 70 leaves remainders of 19, 32, 37 and 53, respectively.

• A. 26,447
• B. 26,446
• C. 26,443
• D. 26,441

Answer 1

Answer:

C. 26,443

Calculate the difference between the divisor and the remainder for each:

(36 - 19) = 17

(49 - 32) = 17

(54 - 37) = 17

(70 - 53) = 17

Common difference = 17

Find the LCM of the divisors: 36, 49, 54, 70.

LCM = 2² × 3³ × 5 × 7²

LCM = 26460

Since the common difference is 17, the required number is:

N = LCM - common difference = 26460 - 17 = 26443