# What is the least common multiple and denominator?

The smallest common multiple (whole number) of two or more whole numbers is called the lowest (or least) common multiple (LCM). For example, for the numbers 3 and 8, the multiples of 8 are 8, 16, 24, 32, and so on; the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, and so on. Therefore, the LCM of 3 and 8 is 24.

The least common denominator (or LCD) is mainly used to carry out the addition or subtraction of fractions. In order to do these operations, the fractions need to have the same denominator. (For more information about fractions, see below.) The easiest way to work on such calculations is to determine the lowest number possible for the denominator—a number called the least common denominator (LCD)—which is actually the common factor by which two numbers are divisible. For example, to add 1/6 and 1/8, we have to find the least common multiple of the denominators. In this case, the number is 24: Multiply 1/6 × 4/4 and 1/8 × 3/3, to change each addend to some number of “24ths”; or 1/6 × 4/4 = 4/24; and 1/8 × 3/3 = 3/24. Thus, 1/6 + 1/8 = 4/24 + 3/24 = (4+3)/24 = 7/24.

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