LCM Calculator

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LCM calculator is used to calculate the least common multiple of two or more numbers. A least common multiple calculator is also referred to as the least common factor calculator. This calculator makes it easy to find the least common multiple of big numbers.

In this post, we will guide you what is least common multiple, how to find LCM, LCM methods, LCM examples, and much more.

What is LCM?

The smallest positive integer divisible by two or more integers x and is known as Least Common Multiple in mathematics. It is commonly denoted as LCM (x, y). LCM is also known as the Lowest Common Multiple.

How to use LCM calculator?

Using the lowest common denominator calculator is easy, but calculating the least common multiple with pen and paper is not that simple. We will explain methods to find the least common multiple in the next section so that you can properly understand the concept. Follow these steps to use the least common denominator calculator.

  • Enter integers in the given input box.
  • Separate each value by using a comma.
  • Press the Calculate button to get the least common multiple of entered integers.

This LCM finder will instantly calculate the LCM and show you the complete table of calculation for your better understanding. If you need to calculate the Greatest Common Divisor, you can use our GCD Calculator.

How to find the Least Common Multiple?

Least Common Multiple can be calculated in several ways. Below are some important methods to find LCM.

Brute Force Method

The Brute Force method is most simple to calculate LCM. You need to write down all multiples of the integers involve in the calculation until both reaches at the common multiple.

Example:

\(\text{Find LCM} (20, 25)\)

Write down the multiples of both integers and find common multiple.
\(20: 20, 40, 60, 80, 100\)
\(25: 25, 50, 75, 100\)

The LCM is 100 in this case because 100 is the common multiple in both integers.

Prime Factorization Method

The prime factorization is a more formal means of finding the LCM of integers. Prime factorization results of splitting each of the numbers into its prime numbers product. The least common multiple is calculated by multiplying each primary number with each other. Common numbers would be considered one time in multiplication. Please note that computing the LCM in this manner is still limited to smaller numbers, although it is more effective than using the brute force method.

Example:

\(\text{Find LCM} (15, 18, 21)\)

Step 1: Write down prime factors of all integers.

\(15: 3 \times 5\)

\(18: 2 \times 3 \times 3\)

\(21: 3 \times 7\)

Step 2: Multiply the biggest numbers of each integer’s prime factors. If a number occurred two or more times, it would be considered one time in multiplication.

\(2 \times 3 \times 3 \times 5 \times 7 = 630\)

So, the LCM is 630.

Prime Factorization using Exponents

LCM can be calculated using exponents on the prime factors of the integers.

  • Write down the prime factors of each integer and its exponents.
  • Identify the number of highest exponent in prime factors of each number.
  • Multiply the identified numbers with the highest exponent to get LCM.

Example:

\(\text{Find LCM} (12, 16, 20)\)

Step 1: Write down the prime factors of each integer with its exponents.

\(12 = 2 \times 2 \times 3 = 2^2 \times 3^1\)

\(16 = 2 \times 2 \times 2 \times 2 = 2^4\)

\(20 = 2 \times 2 \times 5 = 2^2 \times 5^1\)

Step 2: Identify numbers with the highest exponent in prime factors of each integer. In this case:

\(2^4, 3^1, and  5^1\)

Step 3: Multiply these integers to get the LCM.

\(2^4 \times 3^1 \times 5^1 = 240\)

So, the LCM is 240.

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Donald A. Lyons | 22/08/2019

This calculator do exactly what I want. Easy, quick and accurate.

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