bài 1.Tìm hai số tự nhiên biết tích của chúng là 180 và ƯCLN của chúng là 3.
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\(180=2^2\cdot3^2\cdot5\)
Vậy để ước chung lớn nhất của 2 số không quá 3 thì thừa số chung khi phân tích 2 số ra số nguyên tố là 3.
Vậy \(a=2^2\cdot3=12;b=5\cdot3=15\) và \(a=2^2\cdot3\cdot5=60;b=3\)
Vì \(ƯCLN\) của chúng là \(3\) nên:
Ta gọi:
Số lớn là: \(3x\)
Số bé là: \(3y\)
Trong đó \(x\) và \(y\) là hai số nguyên tố cùng nhau \(\left(x>y\right)\)
Theo đề bài ta có:
\(3x.3y=180;xy=20\)
Vì \(x>y\) và \(x,y\) là hai số nguyên tố cùng nhau nên:
\(\left(x,y\right)=\left(20;1\right),\left(5;4\right)\)
Với \(x=20;y=1\Rightarrow x=60;y=3\)
Với \(x=5;y=4\Rightarrow x=15;y=12\)
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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