The greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.
Finding the Solution
To find the greatest 3-digit number divisible by 8, 10, and 12, we first need to find the least common multiple (LCM) of these three numbers.
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Find the LCM: The prime factorization of 8 is 2 x 2 x 2. The prime factorization of 10 is 2 x 5. The prime factorization of 12 is 2 x 2 x 3. The LCM is the product of the highest powers of all prime factors present in the numbers: 2 x 2 x 2 x 3 x 5 = 120.
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Divide the largest 3-digit number: The largest 3-digit number is 999. Dividing 999 by the LCM (120), we get 8.325.
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Find the greatest multiple: The greatest integer less than or equal to 8.325 is 8. Multiplying the LCM (120) by 8 gives us 960.
Therefore, 960 is the greatest 3-digit number exactly divisible by 8, 10, and 12. Multiple sources (Cuemath, Byju's, Toppr, Doubtnut, Brainly, Vedantu, Quora, Teachoo, Quora) confirm this result.
