Question
Find the smallest integer greater than 100 which leaves
remainder 4 when divided by each of 5, 6 and 7.Solution
ATQ, If N leaves remainder 4 when divided by 5, 6, 7, then N − 4 is divisible by all 5, 6, 7. LCM(5, 6, 7): 5 = 5 6 = 2 × 3 7 = 7 LCM = 2 × 3 × 5 × 7 = 210 So N − 4 = 210k ⇒ N = 210k + 4 We want N > 100: 210k + 4 > 100 ⇒ 210k > 96 ⇒ k ≥ 1 Smallest such N is for k = 1: N = 210 × 1 + 4 = 214 Answer: 214.
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