Number Theory problem #71264
Miranda is an avid collector of stamps. She is trying to arrange her collection of stamps into neat rows. She found that when she arranged them in row of 2, 3, 4, 5, 6 or 7, she always came up 1 short.
What is the minimum number of stamps that Miranda has?
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5 solutions
Let Miranda have m stamps. Then, we are given that m + 1 stamps can be arranged in rows of 2, 3, 4, 5, 6 or 7. Hence, m + 1 must be a multiple of 2, 3, 4, 5, 6 and 7, so we want the lowest common multiple.
Since L C M ( 2 , 3 , 4 , 5 , 6 , 7 ) = 2 2 × 3 × 5 × 7 = 4 2 0 , hence the smallest value of m + 1 would be 420, which gives us m = 4 1 9 .