Multiple choice

The least number which when divided by 7, 10, 15 and 21 leaves 5, 8, 13 and 19 respectively as remainders is

  1. 210

  2. 208

  3. 220

  4. 198
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Differences between divisors and remainders: 7-5=2, 10-8=2, 15-13=2, 21-19=2. The constant difference is 2. The number is LCM(7, 10, 15, 21) - 2. LCM(7, 10, 15, 21) = 210. 210 - 2 = 208.

AI explanation

Observe that the difference between the divisor and the remainder is constant: 7 - 5 = 2, 10 - 8 = 2, 15 - 13 = 2, and 21 - 19 = 2. Calculate the least common multiple of the divisors 7, 10, 15, and 21, which is 210. Subtract the common difference of 2 from this LCM to get 208. The required least number is 208.

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