# Math riddle

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I am a two digit number greater than 40.You can divide me by 7 and also by 8, but not any other set of single digit number.what number am I

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Multiples of 7:
49, 56, 63, 70, 77, 84, 91, 98

Multiples of 8:
48, 56, 64, 72, 80, 88, 96

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At first sight, the answer is the LCM (Lowest common multiple) of 7 and 8?

Looking further, there is a problem with the question ("but not any other set of single digit number"). Any number divisible by 8 is also divisible by 2 and 4, hence the two-digit number divisible by 7 and 8 will always be divisible by 7, 8, 4 and 2.

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Thanks, Ms. Sue
Mathmate thanks that's what I thought just wanted to make sure maybe it was a misprint on the riddle.

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I read the problem as the PAIR of numbers that can go into the two digit numbers. The numbers 7 and 8 are the only single digit PAIR of numbers that fit that description.

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Ms Sue, I think your interpretation is very reasonable.

However, mathematically speaking, there is no limit on the number of members in a set. As Paul indicated, there is probably a misprint, where it read "but not any other SET of single digit numbers" it is probably supposed to read "but not any other PAIR of single digit numbers".

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Thanks, MathMate.