SOLUTION: list three digit smallest and largest number which is divided by 8,12 and 16 respectfully

Question 1119569: list three digit smallest and largest number which is divided by 8,12 and 16 respectfully

Answer by ikleyn(52925) (Show Source): You can put this solution on YOUR website!
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list three digit smallest and largest number which is divided by 8,12 and 16 respectfully
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The correct formulation is THIS:

    List three-digit smallest and largest numbers what are divisible by 8, 12 and 16 respectively.

Solution

The Least Common Multiple of the numbers 8, 12 an 16 is 48.


Therefore, the integer numbers that are divisible by 8, 12 and 16 are those and only those that are multiple of 48.


The smallest 3-digit integer multiple of 48 is  144.

    How to find it ? - Divide 100 by 48:   = 2.083 (approximately);

    So, consider 48*3 - it is exactly 144.



The largest 3-digit integer multiple of 48 is  960.

    How to find it ? - Divide 999 by 48:   = 20.81 (approximately);

    So, consider 48*20 - it is exactly 960.



Answer.  The largest 3-digit integer divisible by 8, 12 and 16 is 960.

         The smallest 3-digit integer divisible by 8, 12 and 16 is 144.

Solved.

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