The number of integers that are multiples of both 6 and 10 is infinite. Here are the first few: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300 . . .
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Multiples of 6: 6, 12, 18, 24, 30, 36, ................ Multiples of 10: 10, 20, 30, 40, ................ 30 is the LCM (least common multiple) of 6 and 10. correct but LCM stands for lowest common multiple...
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Common denominators. These are called "common multiples". For example, multiples of 4 are: 4,8,12,16,20,24 ... . Multiples of 6 are: 6,12,18,24,30,36 ... . The numbers on both lists are the common multiples and they include: 12,24,36, ... . Specifically, the smallest number in any such list of common multiples (12 in this example) is known as the Least (or Lowest) Common Multiple or LCM.
There are 10 multiples of 6 in that range.
Multiples of 10 include any number ending in zero. For them to be common, they need to be compared to another set of multiples.