The smallest number such that when it is divided by 8 has a remainder of 6 and when it is divided by 9, has a remainder of 7 is
Possible multiples of 8 and 9 = 72, 144, 216, 288, 360, 432, 576, 648.
\(\frac{387}{8}\) has remainder = 3; \(\frac{387}{9}\) has remainder 0.
\(\frac{493}{8}\) has remainder 5; \(\frac{493}{9}\) has remainder 7.
\(\frac{502}{8}\) has remainder 6; \(\frac{502}{9}\) has remainder 7.
\(\frac{441}{8}\) has remainder 1; \(\frac{441}{9}\) has remainder 0.
\(\frac{634}{8}\) has remainder 2; \(\frac{634}{9}\) has remainder 4.
Hence 502 is the answer.
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