Multiple choice

The smallest number which when divided by 18, 24, 38 and 42 leaves the remainder 15, 21, 35 and 39 respectively is :-

  1. $9579$
  2. $9573$
  3. $9887$
  4. $7305$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a number N leaves remainder r when divided by d, we can write N = d*k + r. Here, each remainder is 3 less than the divisor (18-15=3, 24-21=3, 38-35=3, 42-39=3), so N+3 must be divisible by all four divisors. Therefore, N+3 = LCM(18,24,38,42). LCM = 2^3 × 3^2 × 7 × 19 = 9576, so N = 9576 - 3 = 9573.

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