Question

Determinati toate numerele naturale a si b stiind ca (a b) este egal cu 42 si cmmmc(a b)este egal cu 252.raspuns complet va rog!!

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$\it (a,\ b)=42 \Rightarrow \begin{cases}\it a=42x\\ \\\it b=42y\\ \\\it (x,\ y)=1\end{cases}\ \ \ \ (*)\\ \\ \\ a\cdot b=(a,\ b)\cdot[a,\ b] =42\cdot252=42\cdot42\cdot6 \stackrel{(*)}{\Longrightarrow}\ 42x\cdot42y=42\cdot42\cdot6 \Rightarrow\\ \\ \Rightarrow x\cdot y=6 =1\cdot6=2\cdot3=3\cdot2=6\cdot1 \Rightarrow \begin{cases}\it a=42,\ b=42\cdot6=252\\ \\\it a=42\cdot2=84,\ b=42\cdot3=126\\ \\\it a=42\cdot3=126,\ b=42\cdot2=84\\ \\ \it a=42\cdot6=252,\ b=42\end{cases}$