## Task 1 - 060731

Let $a, b, c$ be natural numbers, where $a$ is divisible by $b$ and $b$ is divisible by $c$.

Determine the least common multiple and the greatest common divisor of the numbers $a, b$ and $c$ for $a \geq 1, b \geq 1, c \geq 1$!
(1) If $p, q$ are natural numbers $\geq 1$, and $p$ is divisible by $q$, then $p$ is the $\operatorname{lcm}$ of $p, q$.

(2) Under the same conditions, $q$ is the $\gcd$ of $p, q$.

(3) The $\mathrm{lcm}$ of $a, b, c$ is the $\mathrm{lcm}$ of $a$ and the $\mathrm{lcm}$ of $b, c$. Thus, according to (1), it is the $\mathrm{lcm}$ of $a$ and $b$. Again, by (1), it follows that it is $a$.

(4) The $\gcd$ of $a, b, c$ is the $\gcd$ of $c$ and the $\gcd$ of $a, b$. Thus, according to (2), it is the $\gcd$ of $c$ and $b$. Again, by (2), it follows that it is $c$.