divisibility

2007-09-26 6:22 pm
what is the least positive number divisible by 9 different prime numbers? why?
a. 111,546,435
b. 203,693,490
c. 223,092,870
d. 3,011,753,745
e. 3,234,846,615

回答 (1)

2007-09-26 7:00 pm
✔ 最佳答案
First of all, not counting 1 as a prime number, we have the smallest 9 prime numbers as:
2, 3, 5, 7, 11, 13, 17, 19 and 23
Since the 9 prime numbers are relatively prime, i.e. having no common factors except 1, their L.C.M. will be:
2 × 3 × 5 × 7 × 11 × 13 × 17 × 19 × 23 = 223092870
which is also the LEAST NUMBER divisible by 9 DIFFERENT PRIME NUMBERS.
So ans = D

2007-09-26 11:04:14 補充:
Sorry, 看錯, ANS 應該係 C.
參考: My Maths knowledge


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