Question
Find the smallest number which when divided by 6, 8 and
9 leaves a remainder of 2 in each case.Solution
If a number N leaves remainder 2 on division by 6, 8, 9, then N − 2 is divisible by 6, 8 and 9. So N − 2 = LCM(6, 8, 9) 6 = 2 × 3 8 = 2³ 9 = 3² LCM = 2³ × 3² = 8 × 9 = 72 So N − 2 = 72 ⇒ N = 72 + 2 = 74
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