Question
Determine the largest four-digit number that is exactly
divisible by 15, 25, 40, and 75.ÂSolution
LCM of 15, 25, 40, 75 15 = 3 × 5 25 = 5² 40 = 2³ × 5 75 = 3 × 5² LCM = 2³ × 3 × 5² LCM = 8 × 3 × 25 LCM = 600 Largest 4-digit number = 9999 Divide: 9999 ÷ 600 = 16.66 Greatest integer multiple = 16 Required number = 600 × 16 = 9600
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