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Determine the sum of all positive three-digit integer numbers that give a remainder 2 when divided by 7, a remainder 4 when divided by 9, and remainder 7 when divided by 12.

 Apr 28, 2019
 #1
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N mod 7 = 2
N mod 9 = 4
N mod 12 = 7, solve for N

The LCM[7, 9, 12] =252
N =252n + 247, where n =0, 1, 2, 3.....etc.
Sum=247 + 499 + 751 = 1,497

 Apr 28, 2019
 #2
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+1

thanks!

Starz  Apr 29, 2019

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