Question
Find the greatest 4-digit number which is exactly divisible by 12, 15 and 21.
Solution
We need a multiple of LCM(12, 15, 21) that is ≤ 9999. Prime factors: 12 = 2² × 3 15 = 3 × 5 21 = 3 × 7 LCM = 2² × 3 × 5 × 7 = 4 × 3 × 5 × 7 = 420 Greatest 4-digit number = 9999 Check how many 420s fit in 9999: 9999 ÷ 420 ≈ 23.8 Largest integer ≤ 23.8 is 23 Required number = 420 × 23 = 9660
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