Question
Find the greatest 4-digit number which is exactly
divisible by 12, 15 and 18.Solution
12 = 2² × 3 15 = 3 × 5 18 = 2 × 3² LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180 Greatest 4-digit number = 9999 Greatest multiple of 180 ≤ 9999: 9999 ÷ 180 ≈ 55.55…, so take 55 Required number = 55 × 180 = 9900
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