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What are common multiples and least common multiples?
All numbers have multiples. Some numbers have some of the same multiples as other numbers. These are known as common multiples. The smallest of these is known as the least common multiple. Common multiples of 3 and 4 include 12, 24, 36 and so on. The LCM of 3 and 4 is 12.
What are the first three common multiples of 2 and 3?
All nonzero numbers have multiples. Some numbers have some of the same multiples as other numbers. These are known as common multiples. 36 is a multiple of 4. 36 is a multiple of 9. 36 is a common multiple of 4 and 9.
What are the multiples of one number that are also multiples of another number?
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.
What are the common multiples of 6 and 2?
The common multiples of 2 and 6 are the infinite set of numbers that are multiples of their LCM, which is 6. So the common multiples of 2 and 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, and so on.
What is the ratio of the number of positive common multiples less than 100 of the numbers 3 and 5 to the number of positive common multiples less than 100 of the numbers 2 and 7?
The LCM of two consecutive numbers is their product. The LCM of two consecutive multiples of 5 is their product divided by 5. Two consecutive numbers cannot be multiples of 5.
