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What is the largest number k less than 1000 such that the remainder is 1 when k is divided by each of 3, 4, and 5?

 Dec 11, 2021
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What is the largest number k less than 1000 such that the remainder is 1 when k is divided by each of 3, 4, and 5?

 

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\(15\times 3\cdot 4\cdot 5=900\\ 16\times 3\cdot 4\cdot 5=960\\ 17\times 3\cdot 4\cdot 5=1020\\ k=16\times 3\cdot 4\cdot 5+1\)

\(k=961\)

laugh  !

 Dec 11, 2021

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