A number theory problem by Paola Ramírez

There is a sack full of potatoes. If potatoes are counted 4 4 by 4 4 , 5 5 by 5 5 , 6 6 by 6 6 or 7 7 by 7 7 always left over 3 3 . The sack has more than 3 3 potatoes and less than 800 800 . How many potatoes have the sack?


The answer is 423.

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1 solution

l c m ( 4 , 5 , 6 , 7 ) = 420 lcm(4,5,6,7)=420 , thus, when there are 423 potatoes, the remainder will be 3 when divided by 4, 5, 6, or 7.

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