GRE
简答题
How many numbers between 1 and 1，000 are either a multiple of 28 0r a multiple of 32？
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B．
The number 28factors int0 2×2×7 and 32 factors int0 2×2×2×2×2，sotheir least common multiple iS 2×2×2×2×2×7=224．Because1．000÷28≈35．7，thereare 35 multiples of 28 from 1 t0 1，000．Because1．000÷32=31．25，there are 31 multiples of 32 from 1 t0 1，000．Because 1．000÷224≈4．5，there are four numbers between 1 and 1，000t11at are multiples of both 28 and 32．This means thatif you count all the multiples of 28 and all the multiples of 32，you will double．count four of tham．Thus there are 35+31—4=62 numbers between 1 and 1，000 that are either a multiple of 28 0r a multiple of 32．
The number 28factors int0 2×2×7 and 32 factors int0 2×2×2×2×2，sotheir least common multiple iS 2×2×2×2×2×7=224．Because1．000÷28≈35．7，thereare 35 multiples of 28 from 1 t0 1，000．Because1．000÷32=31．25，there are 31 multiples of 32 from 1 t0 1，000．Because 1．000÷224≈4．5，there are four numbers between 1 and 1，000t11at are multiples of both 28 and 32．This means thatif you count all the multiples of 28 and all the multiples of 32，you will double．count four of tham．Thus there are 35+31—4=62 numbers between 1 and 1，000 that are either a multiple of 28 0r a multiple of 32．
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