Divide $207$ into three parts such that these parts are in A.P and the product of the two smaller parts is $4623$.
$\because \;$ The three parts are in A.P, let the parts be $\;$ $a - d, \; a, \; a+d$
Product of the smaller parts $= 4623$
i.e. $\;$ $a \left(a - d\right) = 4623$ $\;\;\; \cdots \; (1)$
Sum of the parts $= 207$
i.e. $\;$ $a - d + a + a + d = 207$
i.e. $\;$ $3a = 207$
$\implies$ $a = 69$ $\;\;\; \cdots \; (2)$
Substituting the value of '$a$' from equation $(2)$ in equation $(1)$,
$69 \left(69 - d\right) = 4623$
i.e. $\;$ $69 - d = 67$ $\implies$ $d = 2$
$\therefore \;$ The three parts are $\;$ $67, \; 69, \; 71$