LCM calculator

Least Common Multiple (LCM) is the smallest numbere that is divisible by all given numbers. For example: LCM(8, 6) = 24. This calculator calculate LCM of two or more numbere using 5 different methods. For each method caluclator 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
Finc LCM using prime factors
Find LCM using Ladder Method
Use LCM formula
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 usin 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 formula.

How to find LCM ?

This calculator uses five methods to find Least Common Multiple. We will show them using an 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 factorisation 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 formula

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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213 465 135 solved problems

Problem:

Find Least Common Multiple of 8, 12 and 15 using division method..

Result:

LCM( 8, 12, 15 ) = 120

Explanation:

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

 81215

Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 2.

(if any number is not divisible by 2, write it down unchanged)

281215
 4615

Step 3 : Continue dividing by prime numbers till we get 1 in all columns.

281215
24615
22315
31315
5115
 111

Step 4 : Multiply numbers in first column to get LCM.

LCM( 8, 12, 15 ) = 2 · 2 · 2 · 3 · 5 = 120