Question
What is the smallest 4-digit number that is exactly
divisible by 9, 12 and 15?Solution
Find LCM of 9, 12, 15 9 = 3² 12 = 2² × 3 15 = 3 × 5 LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180 We need smallest 4-digit multiple of 180. 1000 ÷ 180 ≈ 5.55... 180 × 5 = 900 (3-digit) 180 × 6 = 1080 (4-digit) So smallest 4-digit number divisible by 180 is 1080.
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