Bài 12: ƯCLN của hai số là 45 số lớn là 270 Tìm số nhỏ
Bài 13: ƯCLN của hai số là 4 số lớn là 8 Tìm số lớn
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a) goi hai so la a ; b va a >b
vi UCLN(a,b)=18=>a=18k ; b=18q (trong do UCLN (k,q)=1 va k>q)
=>a+b=162
18k+18q =162
18(k+q)=162
k+q=9
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52542000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 542454550212.100000000000000000000000000000000000000000000000000000000000000000000000000000 |
Ư(270)=2.3^3.5
mà ƯCLN=45
=> 3^2.5=45
mà Ư(45)=3^2.5
vậy số thứ 2 là 45
Gọi 2 số đó là a và 270 với a < 270
Ta có:
ƯCLN(a ; 270) = 45
=> a = 45m ; 270 = 45 . 6 (m ∈ N)
Mà :
ƯCLN(a ; 270) = 45
=> ƯCLN(m ; 6) = 1
Do a < 270 nên m < 6.
Vậy m ∈ {1 ; 5}
Khi đó a ∈ {45 ; 225}
Vậy số cần tìm là 45 hoặc 225
UCLN(270 ; a) = 45 => a =45q
270 = 45 .6
=> (q;6) =1 ; q < 6
=> q thuộc {1;5}
+ q =1 => a =45
+q =5 => a =225
Vậy số nhỏ là : 45 hoặc 225