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There is no largest common multiple of any set of numbers as whatever value is assumed to be the largest can be increased by adding the lowest common multiple of the numbers to get an even larger common multiple.

For 2 and 3 the lowest common multiple is 6. So whatever number is assumed to be the largest common multiple it can always be increased by 6 to get a larger common multiple.

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Q: What it is the largest common multiple of two and three?
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