1. $a=215\qquad b=375$
   
   $\begin{array}{rlrlrlr} 375 & = & 1 & \times & 215 & + & 160 \\ 215 & = & 1 & \times & 160 & + & 55\\ 160 & = & 2 & \times & 55 & + & 50\\ 55 & = & 1 & \times & 50 & + & \color{magenta}\boxed{5}\\ 50 & = & 10 & \times & 5 & + & 0\\ \end{array}$ $$a\land b=5\qquad \mbox{et} \qquad a\lor b=\dfrac{ab}{a\land b}=16125$$
   
   
2. $a=2016 \qquad b=375$
   $\begin{array}{rrrlrlr} 2016 & = & 5 & \times & (375) & + & 141\\ 375 & = & 2 & \times & 141 & + & 93\\ 141 & = & 1 & \times & 93 & + & 48\\ 48 & = & 1 & \times & 45 & + & \color{magenta}\boxed 3\\ 45 & = & 15 & \times & 3 & + & 0\\ \end{array}$
   
   $a\land b =3\qquad$ et $\qquad a\lor b=252000$
   
   
3. $a=-49\qquad b=-735$
   
   $\begin{array}{rlrlrlr} 375 & = & 7 & \times & 49 & + & 32\\ 49& = & 1 & \times & 32 & + & 17 \\ 32&=&1&\times& 17&+&15\\ 17& = & 1 &\times & 15 & + & 2\\ 15& = & 7 & \times & 2 & + &{{\color{magenta} \boxed1 }} \\ 2 & = & 2 & \times & 1 & + & 0\\ \end{array}$
   
   $(-49)\land(-735)=1\qquad$ et $\qquad a\lor b=18375$
   
   

Décomposition en facteur premiers:

1. 
   $\qquad (a = 215 \qquad\qquad b = 375)$
   
   $a = 5\times 43 \qquad b = 3\times 5^3$
   
   On tire:
   
   $$(~a\land b =5\qquad \mbox{et}\qquad a\lor b = 3\times 5^3\times 43~)$$
2. 
   
   $a = 2016 \qquad b = -375 $
   
   $a = 2^5\times 3^2\times 7 \qquad b = -3\times 5^3$
   
   On en déduit: $$\left(~a\land b\qquad = 3\qquad \mbox{et}\qquad a\lor b = 2^5\times 3^2\times 5^3\times 7~\right)$$
3. 
   $$\left(~a = -49\qquad\mbox{et}\qquad b=-735~\right)$$ On a: $$-49=-7^2\qquad -735=-3\times 5^3$$ On en déduit: $$\left(~ a\lor b=1\qquad a\land b=3\times 5^3\times 7^2~\right)$$