更新1:
但用短除好似唔得(用20wor)
暑期作業(數學問題)係小六升中一嫁
回答 (7)
2007-07-14 8:49 pm
✔ 最佳答案
先看看30和45的質因子分解式：30=2x3x5
45=3x3x5
如果要使三個數的H.C.F.是5，x一定要是5的倍數但不是3的倍數。
x=5x？
然後，30和45的L.C.M.是2x3x3x5=90。
問題就變成90和x的L.C.M.是180
180=2x2x3x3x5，剛剛比90多了一個2。
要多一個2，就要把2乘兩次，等於2x2x5=20。
20是答案。
參考: 自己的知識
2007-07-15 7:35 am
HCF(x, 30,45) = 5
30=2 * 3 * 5
45=3 * 3 * 5
so x value should contain factor 5 but cannot contain factor 3 for otherwise the HCF=15
LCM(30, 45) = 2 * 3* 5 * 3 = 90
x cannot be 5 or 2*5 for otherwise the LCM=90
Now the LCM is 180 which is =2 * 2 * 3 * 3 * 5
X is 2*2*5 = 20
This is the only possible solution for X because adding more factors to X will mean a higher value of LCM.
30=2 * 3 * 5
45=3 * 3 * 5
so x value should contain factor 5 but cannot contain factor 3 for otherwise the HCF=15
LCM(30, 45) = 2 * 3* 5 * 3 = 90
x cannot be 5 or 2*5 for otherwise the LCM=90
Now the LCM is 180 which is =2 * 2 * 3 * 3 * 5
X is 2*2*5 = 20
This is the only possible solution for X because adding more factors to X will mean a higher value of LCM.
參考: me
2007-07-14 12:16 am
x的可能值是20 ,
因為
20 , 30 , 45 的H.C.F.是 180 ,
L.C.M.也是 180 ,
所以 x 應該等於 20 。
因為
20 , 30 , 45 的H.C.F.是 180 ,
L.C.M.也是 180 ,
所以 x 應該等於 20 。
2007-07-14 12:14 am
Factorization of 30 = 2 x 3 x 5
Factorization of 45 = 3 x 3 x 5
Since HCF is 5 Then The common factor of x with 30 and 45 is 5 only
x = a x b x c x.... x 5
180 = 30 a = 45 b = x c, where a,b and c are relatively prime
a = 6, b =4, c must not be a even number
c=1 ,x=180, then the factorization of x will contain 3 and 5, X
c=3, x=60, then the factorization of x will contain 3 and 5, X
c=5, x= 36, there is no 5 in x, X
c=9, x=20, then the factorization of x is 2 x 2 x 5, ok
c=15, x=15, then the factorization of x will contain 3 and 5, X
c=45, x=4, there is no 5 in x, X
Then x is 20
Factorization of 45 = 3 x 3 x 5
Since HCF is 5 Then The common factor of x with 30 and 45 is 5 only
x = a x b x c x.... x 5
180 = 30 a = 45 b = x c, where a,b and c are relatively prime
a = 6, b =4, c must not be a even number
c=1 ,x=180, then the factorization of x will contain 3 and 5, X
c=3, x=60, then the factorization of x will contain 3 and 5, X
c=5, x= 36, there is no 5 in x, X
c=9, x=20, then the factorization of x is 2 x 2 x 5, ok
c=15, x=15, then the factorization of x will contain 3 and 5, X
c=45, x=4, there is no 5 in x, X
Then x is 20
2007-07-13 11:41 pm
x=20
Factors:-
20=1,2,4,5,10
30=1,2,3,5,6,10,15,30
45=1,3,5,9,15,45
Multiples:-
20=20,40,60,80,100,120,140,160,180.....etc
30=30,60,90,120,150,180....etc
45=45,90,135,180...etc
Factors:-
20=1,2,4,5,10
30=1,2,3,5,6,10,15,30
45=1,3,5,9,15,45
Multiples:-
20=20,40,60,80,100,120,140,160,180.....etc
30=30,60,90,120,150,180....etc
45=45,90,135,180...etc
參考: me
收錄日期: 2021-04-24 09:27:38
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070713000051KK02427