Multiple choice

If x be the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder . The product of the digits of the number x is

  1. 18

  2. 48

  3. 24

  4. 144
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

LCM of 5,6,7,8 = 840. Number x = 840k + 3. Also x divisible by 9: 840k + 3 ≡ 0 (mod 9). Since 840 ≡ 3 (mod 9), we get 3k + 3 ≡ 0 → k = 2 (minimum). So x = 840(2) + 3 = 1683. Product of digits = 1 × 6 × 8 × 3 = 144. The number must satisfy all congruence conditions simultaneously.

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