一條數學題~HELP

因為佢地既HCF係5
1.咁X一定係5既倍數
2.同時X亦要可以俾180整除
咁先定一個5既倍數
Let x be 5
如果X=5既話,X,30,45既LCM就唔需要係180 90已經可以
咁即係要搵1個數係5既倍數亦唔可以俾90整除&可以俾180整除<
5既倍數 5,10,15,20,25,30
5,10,15都可以俾90整除 所以唔會係
而20就符合以上既條件
所以X最細既數係20
同埋第1個講X=30係錯==
如果X=30 LCM係90

In H.C.F,
Because X,30 and 45的Ｈ.C.F. is５

X may be 5,10,20,25,35,40.........(The multiple of 5)

In L.C.M,
180/5=36
180/10=18
180/20=9
180/25=7.2
180/35=5.14....
180/40=4.5

So,we can find that X is 5,10 and 20

Because L.C. M. is 180 and H.C.F.is 5.
We can know that X, 30, 45 can be divided by 5 and suppose the result are Y, 6, 9.
Then because the H.C.F. is 5, so Y,6,9 do not have any common factors.
Next step, divided 6 and 9 by 3, we got the result are 2 and 3.
Because 2 and 3 are no more common factors there we know that 180 is got by from
5 X 3 X Y X 2 X 3. So we got Y is 2 and X=5 mutifly 2=10

X應該係30
因為30,30和45 ge H.C.F係5, L.C.M係180