暑期作業(數學問題)係小六升中一嫁

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。

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.

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 。

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

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

20

30同45ge LCM 係90
咁X就一定唔係5 10 15
20就岩岩好了

應該係 x=20
係咪要埋公式?