Answer:
Multiple of a Number Defined
When you learned your times tables in grammar school, you were learning multiples. For examples, 2, 4, 6, 8, and 10 are multiples of 2. To get these numbers, you multiplied 2 by 1, 2, 3, 4, and 5, which are integers. A multiple of a number is that number multiplied by an integer. Integers are negative as well as positive, so other multiples of 2 are -2, -4, -6, -8 and -10. Would 5x3.1 be considered a multiple? Yes, because even though 3.1 is not an integer, it is multiplied by an integer so 5x3.1 would be considered a multiple of 3.1.
What is the Least Common Multiple?
If you have ever found a common denominator for two or more fractions, you have found a common multiple. For example, if you want to add 3/8 and 5/12, you must find a common denominator. A common denominator, which is another name for common multiple, is a number that is a multiple for all the numbers being considered. For example, a common multiple for 8 and 12 is 24. This means that there is an integer times 8 that will make 24 and there is an integer times 12 that will make 24. Going through the 8 time tables, 8 x 3 = 24 and going through the 12 time tables, 12 x 2 = 24.
These are not the only common multiples for 8 and 12, however. There are countless more. For example, 72 is another common multiple because 8 x 9 = 72 and 12 x 6 = 72. The number 24, however, is special because it is the smallest or lowest or least common multiple for 8 and 12. The number 24 is called the least common multiple, abbreviated LCM, for 8 and 12.
