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## About the calculation of Least common multiple(Three numbers)

Enter the three numbers for which you want to calculate the least common multiple and click the "Calculate Least Common Multiple" button to display the least common multiple of the entered values.

It also shows how to find the least common multiple using prime factorization and how to calculate it using long division.

Please enter an integer between 2 and 10,000,000,000,000,000.

## What is the least common multiple?

A multiple is an integer multiple of another number. For example, if a number is a multiple of 2, you get integer multiples of 2, which become 2, 4, 6, 8, and so on, infinitely.

A multiple that is common to two or more integers is called a common multiple, and the smallest of these is called the least common multiple.

For example, suppose you want to find the least common multiple of 2, 3, and 4.

To get multiples of 2, multiply 2 by 1, 2, etc., you get "2, 4, 6...", and to get multiples of 3, you get "3, 6, 9...".

Multiple of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...

Multiple of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27...

Multiple of 4: 4, 8, 12, 16, 20, 24, 28, 32...

Among these multiples, the common multiples such as 12 and 24 are common multiples of 2, 3, and 4, and the smallest of these, 12, is the least common multiple of 2, 3, and 4.

## How to calculate the least common multiple

To calculate the least common multiple, you can either factorize each number into prime factors or divide them by a common prime number.

Example: Calculate the least common multiple of 10, 12, and 18.

### 1. How to calculate using prime factorization

Factorize each of them into prime factors.

10 = 2 × 5

12 = 22 × 3

18 = 2 × 32

Write out the larger exponent of each prime number and calculate the product.

Therefore, the least common multiple is 22 × 32 × 5 = 180.

### 2. How to calculate by long division

Calculate the least common multiple using long division.

List the numbers for which you want to calculate the least common multiple, and write prime numbers on the left that are divisible by two or more of those numbers.

Since it is divisible by 2, write 2 on the left.

 2 10 12 18

Under each number, write the quotient when divided by the number on the left.

Here we write 5, 6, and 9, each divided by 2.

 2 10 12 18 5 6 9

Keep dividing each number until there are no prime numbers that are divisible by two or more.

If it is not divisible, just write the same number underneath without dividing.

Once you've finished dividing, multiply the number on the left by the number in the L-shape on the bottom number to get the least common multiple.

 2 10 12 18 3 5 6 9 5 2 3

Therefore, the least common multiple is 2 × 3 × 5 × 2 × 3 = 180.

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