a724b¯¯¯¯¯¯¯¯¯¯¯¯⋮12

.So we have :

+ a724b¯¯¯¯¯¯¯¯¯¯¯¯⋮4⇒4b¯¯¯¯¯⋮4⇒b=0;4;8

+a724b¯¯¯¯¯¯¯¯¯¯¯¯⋮3⇒13+a+b⋮3

If b = 0,then ab = 0

If b = 4,then 17+a⋮3⇒a=1;4;7⇒ab=4;16;28

If b = 8,then 21+a⋮3⇒a=0;3;6;9⇒ab=0;24;48;72

Hence,the maximum value of ab is 72 (only when a = 9 ; b = 8)

\(\overline{a724b}⋮12\).So we have :

+ \(\overline{a724b}⋮4\Rightarrow\overline{4b}⋮4\Rightarrow b=0;4;8\)

+\(\overline{a724b}⋮3\Rightarrow13+a+b⋮3\)

If b = 0,then ab = 0

If b = 4,then \(17+a⋮3\Rightarrow a=1;4;7\Rightarrow ab=4;16;28\)

If b = 8,then \(21+a⋮3\Rightarrow a=0;3;6;9\Rightarrow ab=0;24;48;72\)

Hence,the maximum value of ab is 72 (only when a = 9 ; b = 8)