** Posted On** 2017-01-16

** Answer** The smallest required number is 1662.
The equation satisfying the above condition will be: 13a+11=15b+12=17c+13
Equating the first two, we get possible values of (a,b) as
(7,6)
(22,19)
(37,32)
.
.
.
(112,97)
(127,110.
Equating the first and third expressions we get
(a,c)
=(8,6)
(25,19)
(42,32)
.
.
.
(110,84)
(127,97)
The required smallest number= 1662,
For a = 127, b = 110, c = 97

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