Factors create multiples, multiples break down into factors.
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2 and 5 are the prime factors that are common to all multiples of 10.
There are no greatest common multiples only greatest common factors
Multiples of 5 and 10 are called common multiples.
147 and 2500 have no common factors other than 1, so their common multiples are their product, 367,500, and all multiples of 367,500 (735,000, 1,102,500, 1,470,000, 1,837,500, etc.).
Factors go into numbers, numbers go into multiples.