Question

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

Answer 1

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.

Answer 2

Find LCM:

5 = 5

7 = 7

9 = 3²

LCM = 3² x 5 x 7 = 315

-

Greatest 3-digit number:

Greatest 3-digit number = 999

-

Find greatest 3-digit number divisible by 315:

999 ÷ 315 = 3 remainder 54

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

-

Answer: 945