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What is the least number when divided by 3, 5, 8, 9 and 15 leaves a remainder of 2 in each case, but when divided by 19 leaves no remainder?

What is the least number when divided by 3, 5, 8, 9 and 15 leaves a remainder of 2 in each case, but when divided by 19 leaves no remainder? Correct Answer 722

LCM of 3, 5, 8, 9 and 15 is 360. The required number is of the form 360*k+2. The least value of k for which 360*k+2 is divisible by 19 is 2. Hence, the required number is 360*2+2 = 722.

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