Question
Find the greatest 4‑digit number which is exactly divisible by 12, 15 and 20.
Solution
LCM(12, 15, 20): 12 = 2² × 3 15 = 3 × 5 20 = 2² × 5 LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60 Greatest 4‑digit number = 9,999 Divide by 60: 9,999 ÷ 60 = 166 remainder 39 Largest multiple = 60 × 166 = 9,960 Answer: 9,960.
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