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LCM calculator

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LCM calculator computes The Least Common Multiple of two or more numbers using five methods. (division method, listing multiples method, prime factors, ladder method and the LCM formula). The calculator shows a full step-by-step solution of each method, along with a Venn diagram.

Tutorial

What is the Least Common Multiple?

LCM of 6 and 10

The least common multiple (LCM) is the smallest number that can be divided by all the given numbers. For example, LCM(8, 6) = 24, because 24 is divisible by 8 and 6, and it is the smallest such number.

How to calculate LCM

There are five common methods for calculating LCM. We'll use simple examples to show how to apply each of these methods.

5 LCM Methods

1: Listing Multiplies

Example 1: Find LCM of 8 and 6 using listing multiples method.

Step 1: The first few multiples of 6 and 8 are:

List multiples of 6: 6, 12, 18, 24, 30

List multiples of 8: 8, 16, 24, 32, 40

Step 2: LCM is the smallest number that appears in both lists:

LCM (6, 8) = 24

This method is unsuitable for numbers that are greater than 20.

2: Prime factors method

Example: Find the LCM of 8, 12 and 30.

Step 1: Prime factorizations of given numbers are:

8 = 2 · 2 · 2

12 = 2 · 2 · 3

30 = 2 · 3 · 5

Step 2: Match primes vertically

8 = 2 · 2 · 2    
12 = 2 · 2 ·   3  
30 = 2 ·     3 · 5

Step 3: Bring down numbers in each column and multiply to get LCM:

8 = 2 · 2 · 2    
12 = 2 · 2 ·   3  
30 = 2 ·     3 · 5
LCM = 2 · 2 · 2 · 3 · 5 = 120

The Venn diagram below illustrates this solution.

Venn diagram illustrating LCM of numbers 8, 12 and 30.

3: Ladder method

Example: Find the LCM of 84 and 112, using Ladder method.

Step 1: Put the numbers in the division bar as follows:

84 112

Step 2: Divide both 84 and 112 by 2:

2 84 112
42 56

Step 3: Repeat Step 2 until you can no longer divide.

2 84 112
2 42 56
7 21 28
  3 4

Step 4:LCM is the product of numbers into a L shape.

2 84 112
2 42 56
7 21 28
  3 4

LCM = 2 · 2 · 7 · 3 · 4 = 336

4: Division method

Example: Find LCM of 18, 24 and 60 using the division method.

Step 1: Write the given numbers on a horizontal line.

18 24 60

Step 2: Divide the numbers by the smallest prime number. If a number is not divisible by two, write it down unmodified.

18 24 60
2 9 12 30
2 9 6 15
2 9 3 15

Step 3:Continue dividing by larger primes 3, 5, 7… Stop when the last row contains only ones.

18 24 60
2 9 12 30
2 9 6 15
2 9 3 15
3 3 1 5
3 1 1 5
5 1 1 1

Step 4:To get the LCM, multiply the numbers in the first column.

LCM(18,24,60) = 2·2·2·3·3·5 = 360

LCM formula

The formula to find LCM is:

LCM(a,b)·GCD(a,b) = a·b

Example: find LCM of 48 and 60?

Since GCD(48, 60) = 12, we have:

LCM(a,b) · GCD(a,b) = a · b
LCM(a,b) · 12 = 48 · 60
LCM(a,b) · 12 = 2880
LCM(a,b) = 2880/12
LCM(a,b) = 240

LCM Calculator
Five methods each with its own steps
help ↓↓ examples ↓↓
12,20
15,35,14
Prime factors method (default)
Division method
Listing multiples method
Ladder (cake) method
LCM formula
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Examples
ex 1:
Find the lowest number that is divisible by 12 and 15.
ex 2:
Calculate the LCM of 15, 140 and 32 using the prime factorization method.
ex 3:
Find the least common multiple of 18, 15, 96 and 102 using the ladder method.
ex 4:
Find the least common multiple of 204 and 315 using the LCM formula.
Find more worked-out examples in our database of solved problems.
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