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Least Common Multiple Calculator

How to use the tool

To calculate the least common multiple enter the numbers in the fields below and press calculate:

Number 1: Number 2: Number 3: Number 4: Number 5:
Result:
LCM(8, 12, 18) = 23. 3 2= (2.2.2).(3.3) = 8 . 9 = 72
GCD(8, 12, 18) = 2

What is Least Common Multiple?

The Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. In other words, it is the smallest number that can be divided by another without leaving a remainder.

For example, the least common multiple of 12 and 15 is 60 because 60 is the smallest number divisible by 12 and 15. This means that 60 is the smallest number that can represent 12 and 15.

MMC is useful in many areas of mathematics, such as number theory, modular arithmetic, and geometry. It is also important in practical applications such as calculating the common frequency of periodic events and determining the length of the shortest common period of different events.

How to calculate LCM of 2 or more numbers

To calculate the LCM of two or more numbers by prime factors, you first need to find the list of prime factors for each number. You then compare the lists and multiply the common factors by the greatest number of times.

Follow the steps below to calculate the LCM of two numbers "a" and "b":

  1. Find the list of prime factors for "a" and "b". For example, for a = 50 and b = 90:

    2. A = 2 * 5 * 5 = 2 * 52
    B = 2 * 3 * 3 * 5 = 2 * 32 * 5

  2. The next step is to separate the factors, take the ones that appear in only one of the two lists (32), if the factor appears in 2 or more lists, select the one with the highest power (2 and 52)
  3. Having separated the common factors, now solve for their product and you get: LMM(50, 90) = 2 * 32 * 52 = 450 li>
  4. The result of the LCM of 50 and 90 equals 450.

See also