LCM of Two or More Numbers Calculator

1. What is the least common multiple of 20 15 and 11?

The LCM of 20, 15 and 11 will be 660.

2. How do you do LCM step by step?

First, note down the multiples of the numbers for which you want to find out the LCM. Now mark down the common multiples from both. Now identify the smallest multiple, it will be the LCM of the selected two numbers.

3. What is the least common multiple of 42 28 and 14?

The LCM of 42 28 and 14 will be 84.

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers, is the smallest positive integer that is divisible by both a and b.

Or it is the smallest number that can be divided by those numbers without leaving a remainder. 

LCM of Two or More Numbers Calculation With Steps using Manual Methods

Brute Force Method

It is also known as theListing Multiple Method. In this method, each number is listed until the discovery of a common multiple. To evaluate the LCM of the two numbers A and B by the brute force method, the steps are:

1. Firstly, note down the first few multiples of A and B.
2. Differentiate the common multiples from the multiples of both numbers.
3. Choose the smallest common multiple. 
4. Finally, This lowest common multiple is the LCM of the two numbers.

Prime Factorization Method

By using the prime factorization method we can find out the LCM of any given number with the steps given below:

1. Firstly, note down the prime factors of the given numbers by the repeated division method.
2. Write the numbers in their exponential form. Evaluate the product of only those prime factors that have the highest power.
3. Finally, The product of these factors with the highest powers is the LCM of the given numbers. 

Greatest Common Divisor Method

The least common multiple can be evaluated from the greatest common divisor (gcd) with the formula

1: Firstly, evaluate the greatest common divisor (GCD) of integers a and b by any of the following methods

• Prime Factorization
• Division by primes
• Euclidean Algorithm (Euclid's Algorithm)

2:Now, calculate the LCM using the following formula.

LCM(a, b)= |a|.|b| / gcd(a, b)

here, the result of the division is always an integer.

3: Finally, the result is LCM.

Note - This formula is also useful when exactly one of a and b is equal to 0 since gcd(a, 0) = |a|. However, if both a and b are equal to 0, this formula will cause division by zero. Thus, lcm(0, 0) = 0 must be regarded as a special case.

LCM of Two or More Numbers Calculation With Solution

Example: 

Find the LCM of 25, 15, and 30 by the Brute force method.

Solution: 

Firstly, note down the first few multiples of all the three numbers, This will be:

Multiples of 25 = 25, 50, 75, 100, 125...

Multiples of 15 = 15, 30, 45, 60, 75, 90, 105...

Multiples of 30 = 30, 60, 90, 120...

Now, among the common multiples of 25, 15 and 30, 150 is the least multiple that is common in all three numbers. 

Finally, the LCM of 25, 15 and 30 is 150.

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