Show that lcm$(a,b)= ab$ if and only if gcd$(a,b)=1$ Not sure how to begin. If gcd$(a,b)=1$ what can I deduce from that?

It is known that:
$$gcd(a,b) \cdot lcm(a,b)=a \cdot b $$


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*IF $gcd(a,b)=1$:
$$ gcd(a,b) \cdot lcm(a,b)=a \cdot b  \Rightarrow 1 \cdot lcm(a,b)=a \cdot b \Rightarrow lcm(a,b)=a \cdot b$$

*IF $lcm(a,b)=a \cdot b$:
$$gcd(a,b) \cdot lcm(a,b)=a \cdot b \Rightarrow gcd(a,b) \cdot a \cdot b=a \cdot b \Rightarrow gcd(a,b)=1 $$

