SOLUTION: what is the least common multiple and the greatest common factor of 125, 235 and 270?

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Question 563995: what is the least common multiple and the greatest common factor of 125, 235 and 270?
Answer by KMST(5328) About Me  (Show Source):
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The prime factorizations are
125=5%5E3
235=5%2A47
270=2%2A5%2A3%5E3
The numbers 2, 3, and 47 do not appear in all factorizations.
The only common factor is 5.
All three numbers are multiples of 5, but not of 5%5E2, or 5%5E3.
So, the greatest common factor is 5.
The factorization of a common multiple must contain at least
5%5E3, 47, 2, and 3%5E3,
all prime factors with the largest exponents.
The least common multiple is
LCM=2%2A3%5E3%2A5%5E3%2A47=317250
All the other common multiples are multiples of 317250.