# What is the greatest three-digit number which is exactly divisible by 12,14and 15?

We need to find the LCM for the Greatest three-digit numbers

$12 = 2 \times 2\times 3 \\ 14 = 2 \times 7 \\ 15 = 5 \times 3 \\ LCM = 2\times 2 \times 3 \times 5 \times 7 \\ LCM = 420 \\$

Hence, the greatest three-digit numbers = 420

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