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