LCM calculator

Find LCM by listing multiples

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

Step 1: The 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 unsuitable for numbers that are greater than 20.

Find LCM using prime factors

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

This solution can be visualized using a Venn diagram.

Find LCM using the ladder method

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

Step 1: Place the numbers inside the 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

Find LCM using 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 numbers by the 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 the numbers in the first column to get LCM

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:

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