我唔明白,一條問題

180 = 2^2 * 3^2 * 5
30 = 2 * 3 * 5
45 = 3^2 * 5

X can be 2^0 * 3^0 * 5 = 5, or
2^0 * 3 * 5 = 15, or
2^0 * 3^2 * 5 = 45, or
2 * 3^0 * 5 = 10, or
2 * 3 * 5 = 30, or
2 * 3^2 * 5 = 90, or
2^2 * 3^0 * 5 = 20, or
2^2 * 3 * 5 = 60, or
2^2 * 3^2 * 5 = 180

X = 15 ; x = 30, x = 45, x = 60; x = 90; x = 180 are rejected
because LCM = 5 but not = 15;
Thus x = 5 or 10 or 20.

希望幫到你.

2007-08-28 15:11:05 補充：
幫到你嗎?

2007-08-30 21:08:59 補充：
Except x = 20, all others are rejected.Ans. x = 20

180 = 2^2 * 3^2 * 5
30 = 2 * 3 * 5
45 = 3^2 * 5

If x = 2^0 * 3^0 * 5 = 5, HCF (5,30,45) = 5; LCM (5,30,45) = 90;
If x = 2^0 * 3 * 5 = 15, HCF (15,30,45) = 15; LCM (15,30,45) = 90;
If x = 2^0 * 3^2 * 5 = 45, HCF (45,30,45) = 15; LCM (45,30,45) = 90;
If x = 2 * 3^0 * 5 = 10, HCF (10,30,45) = 5; LCM (10,30,45) = 90;
If x = 2 * 3 * 5 = 30, HCF (30,30,45) = 15; LCM (30,30,45) = 90;
If x = 2 * 3^2 * 5 = 90, HCF (90,30,45) = 15; LCM (90,30,45) = 90;
If x = 2^2 * 3^0 * 5 = 20, HCF (20,30,45) = 5; LCM (20,30,45) = 180;
If x = 2^2 * 3 * 5 = 60, HCF (60,30,45) = 15; LCM (60,30,45) = 180;
If x = 2^2 * 3^2 * 5 = 180, HCF (180,30,45) = 15; LCM (180,30,45) = 180;
Except x = 20, all others are rejected.
Ans. x = 20