Question

太好玩了o(^▽^)o

不好意思請問這題怎麼解？

( ) 3.設a、b均爲正整數,且a:b=7:13,若(a,b)+(a,b]=1104,則a+b=?
(A)270 (B)240 (C)210 (D) 150
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Answer 1

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假設 a = 7k, b = 13k
則 (a, b) = k
[a, b] = 7*13*k = 91k

k + 91k = 1104
=> k = 12

=> a = 7k = 84, b = 13k = 156

a + b = 84 + 156 = 240

也可以 a + b = 7k + 13k = 20k = 240