Question
Find the greatest 3-digit number which is exactly divisible by 8, 9 and 12.
Solution
We need the greatest 3-digit multiple of LCM(8, 9, 12). Prime factors: 8 = 2³, 9 = 3², 12 = 2² × 3 LCM = 2³ × 3² = 8 × 9 = 72 Greatest 3-digit number = 999 999 ÷ 72 = 13 remainder 63 Largest multiple = 72 × 13 = 936
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