Question
Find the least number greater than 100 which leaves a
remainder of 4 when divided by 5, 6, and 7.Solution
We want N such that: N ≡ 4 (mod 5), N ≡ 4 (mod 6), N ≡ 4 (mod 7) Then (N − 4) is divisible by 5, 6, and 7 LCM(5, 6, 7) = 2 × 3 × 5 × 7 = 210 So N − 4 = 210k ⇒ N = 210k + 4 Smallest N > 100: For k = 1: N = 210 + 4 = 214 (> 100) Answer: 214
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