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Question 4

Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.


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    Solution

    The least common multiple (LCM) of 2 or more numbers is the smallest number that they all divide evenly.

    LCM:

    26,8,1223,4,623,2,333,1,31.1,1

    LCM of 6, 8 and 12 = 2×2×2×3 = 24
    The smallest 3-digit number = 100
    To find the smallest 3-digit number possible we have to look for smallest 3-digit multiples of 24.
    Multiples of 24 = 24, 48, 72, 96, 120, 144...
    Clearly, 120 is the smallest 3-digit multiple of 24.
    Therefore, the required number is 120.


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