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.
This calculator uses five methods to find Least Common Multiple. We will show them using an examples.
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.
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 |
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
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
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:
$$ \text{LCM(48, 60)} = \dfrac{ 48 \cdot 60 }{ \text{GCD(48, 60)} } = \dfrac{2880}{12} = 240$$Quick Calculator Search
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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.
8 | 12 | 15 |
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)
2 | 8 | 12 | 15 |
4 | 6 | 15 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 8 | 12 | 15 |
2 | 4 | 6 | 15 |
2 | 2 | 3 | 15 |
3 | 1 | 3 | 15 |
5 | 1 | 1 | 5 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 8, 12, 15 ) = 2 · 2 · 2 · 3 · 5 = 120