Least Common Multiple calculator

Least common multiple (LCM) calculator. LCM is also known as least common denominator (LCD).

LCM calculator

First number:
Second number:
Least common multiple (lcm):
Greatest common divisor (gcd):

LCM example

Find the least common multiple number for numbers 8 and 12:

The multiples of 8 are:

8, 16, 24, 32, 40, ...

The multiples of 12 are:

12, 24, 36, 48, ...

So the least common multiple number is 24:

lcm = 24

Here we discuss list of online math calculators that help us for doing calculation easily.

Least Common Multiple

LCM calculator uses two or more numbers and calculates the least common multiple, i.e. the smallest positive integer which is divisible by each one of these numbers. It is an online mathematical tool specially programmed to find out the LCM of two or more integers.

It is necessary to follow the next steps:

1. Enter two or more numbers in the box. These numbers must be integers and may be separated by commas. The values can be copied from a text document or a spreadsheet;

2. Press the "GENERATE WORK" button to make the computation;

3. LCM calculator will give the least common multiple of two or more numbers.

The Least Common Multiple (LCM) is also referred to as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30. The LCM of two or more numbers is the smallest number that is evenly divisible by all numbers in the set.

What is the Least Common Multiple (LCM)?

In mathematics, the least common multiple, also known as the lowest common multiple of two (or more) integers a and b, is the smallest positive integer that is divisible by both. It is commonly denoted as LCM(a, b).

Brute Force Method

There are multiple ways to find a least common multiple. The most basic is simply using a "brute force" method that lists out each integer's multiples.

EX: Find LCM(18, 26)

18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234

26: 52, 78, 104, 130, 156, 182, 208, 234

As can be seen, this method can be fairly tedious, and is far from ideal.

Prime Factorization Method

A more systematic way to find the LCM of some given integers is to use prime factorization. Prime factorization involves breaking down each of the numbers being compared into its product of prime numbers. The LCM is then determined by multiplying the highest power of each prime number together. Note that computing the LCM this way, while more efficient than using the "brute force" method, is still limited to smaller numbers. Refer to the example below for clarification on how to use prime factorization to determine the LCM:

EX: Find LCM(21, 14, 38)

21 = 3 × 7

14 = 2 × 7

38 = 2 × 19

The LCM is therefore:

3 × 7 × 2 × 19 = 798

Greatest Common Divisor Method

A third viable method for finding the LCM of some given integers is using the greatest common divisor. This is also frequently referred to as the greatest common factor (GCF), among other names. Refer to the link for details on how to determine the greatest common divisor. Given LCM(a, b), the procedure for finding the LCM using GCF is to divide the product of the numbers a and b by their GCF, i.e. (a × b)/GCF(a,b). When trying to determine the LCM of more than two numbers, for example LCM(a, b, c) find the LCM of a and b where the result will be q. Then find the LCM of c and q. The result will be the LCM of all three numbers. Using the previous example:

EX: Find LCM(21, 14, 38)

GCF(14, 38) = 2

LCM(14, 38) = 38 × 14/2= 266

GCF(266, 21) = 7

LCM(266, 21) = 266 × 21/7 = 798

LCM(21, 14, 38) = 798

Note that it is not important which LCM is calculated first as long as all the numbers are used, and the method is followed accurately. Depending on the particular situation, each method has its own merits, and the user can decide which method to pursue at their own discretion.

 

---