Question
Find the smallest number greater than 300 which leaves a
remainder 1 when divided by 4, 5 and 6.Solution
Let the number be N. N ≡ 1 (mod 4), (mod 5), (mod 6) So (N − 1) is divisible by 4, 5 and 6 LCM(4, 5, 6) = 60 So, N − 1 = 60k N = 60k + 1 Smallest N > 300: 60 × 5 = 300 → 300 + 1 = 301 (not greater than 300? it is greater) So, N = 301 Answer: 301
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