There is really no such thing as a "greatest common multiple". Once you find the least common multiple of a set of numbers, you can keep adding the LCM to itself over and over again. Each new number you get will be a common multiple of your set of numbers, but each new number will always be larger than the previous. This means that you can keep adding while the number approaches infinity and you will still never find a greatest multiple.
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The greatest common multiple of any set of integers is infinite.
850 is not the greatest common factor of 85 and 10. The person answering the question about the numbers with 850 as the greatest common factor was apparently thinking about the factors of 850 itself, not numbers that would have 850 as their greatest common factor. The greatest common factor of 10 and 85 is 5. The least common multiple of 10 and 85 is 170. The product of 10 and 85 is 850.
The Least Common Multiple of 17 and 85 is 85.
The Greatest Common Divisor of 85, 102 is 17.
The Least Common Multiple (LCM) of 34 and 85 is 170.