Multiple choice

A natural number, when divided by 9, 10, 12 and 15 leaves a remainder of 3 in each case. What is the smallest such number?

  1. 183

  2. 199

  3. 218

  4. 177
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A number leaving remainder 3 when divided by 9, 10, 12, and 15 must be of form LCM(9,10,12,15)k + 3. LCM(9,10,12,15) = 2² × 3² × 5 = 180. The smallest such number is 180×1 + 3 = 183. Distractor 177 = 180-3 (wrong sign) and 199, 218 don't fit the pattern.

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