What is the greatest positive three-digit integer that is divisible by 5, 7 and 9?

First, we want to see what the product of the three numbers is:

9 * 7 * 5 = 315

From there, we can find multiples of 315 to get the largest 3 - digit number divisible by 9, 7, and 5.

315, 630, 945, 1260 ...

The largest is 945.

Find LCM:

5 = 5

7 = 7

9 = 3²

LCM = 3² x 5 x 7 = 315

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Greatest 3-digit number:

Greatest 3-digit number = 999

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Find greatest 3-digit number divisible by 315:

999 : 315 = 3 remainder 54

Greatest 3-digit number divisible by 315 = 315 x 3 = 945.

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Answer: 945