LCM calculator

Least Common Multiple (LCM) is the smallest number that is divisible by all given numbers. For example: LCM(8, 6) = 24. This calculator computes LCM of two or more number using 5 different methods. For each method calculator will show detailed step by step explanation.

Least Common Multiple (LCM) Calculator
five methods with steps for each of them
show help ↓↓ examples ↓↓
Division method
Listing multiples method
Find LCM using prime factors
Find LCM using Ladder Method
Use LCM formulae
working...
examples:
example 1:ex 1:
Find the lowest number which is divisible by 12 and 15?
example 2:ex 2:
Find the LCM of 15, 140 and 32 using prime factorization method.
example 3:ex 3:
Find the least common multiple of 18, 15, 96 and 102 using ladder method.
example 4:ex 4:
Find the least common multiple of 204 and 315 using LCM formulae.

How to find LCM ?

This calculator uses five methods to find Least Common Multiple. We will show them using few examples.

Method 1 : Listing Multiples

Example: find LCM of 8 and 6 by listing multiples.

Step 1: First few multiples of 6 and 8 are:

Multiples of 6: 6, 12, 18, 24, 30

Multiples of 8: 8, 16, 24, 32, 40

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

LCM (6, 8) = 24

Note:This method is not suitable for numbers that are greater than 20.

Method 2 : Find LCM using prime factors

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

Step 1: prime factorization 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

Method 3 : Division Method Ladder Method

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

Step 1: Place the numbers inside division bar:

84 112

Step 2: Divide both numbers 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 a product of numbers into L shape.

2 84 112
2 42 56
7 21 28
  3 4

LCM = 2 · 2 · 7 · 3 · 4 = 336

Method 4 : Division method

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

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

18 24 60

Step 2: Divide numbers with smallest prime number. If any number is not divisible by 2 write it down unchanged.

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

Step 3:Continue dividing by prime numbers 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:Multiply numbers in first column to get LCM

LCM(18, 24, 60) = 2 · 2 · 2 · 3 · 3 · 5 = 360

Method 5: LCM formulae

Example: find LCM of 48 and 60?

In this section we use formula

$$ \text{LCM(a,b)} = \dfrac{ a \cdot b }{ \text{GCD(a,b)} } $$

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

$$ \text{LCM(48, 60)} = \dfrac{ 48 \cdot 60 }{ \text{GCD(48, 60)} } = \dfrac{2880}{12} = 240$$

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