# LCM - Least Common Multiple

## Find the lowest common multiple of numbers. Learn about lcm by division method, lcm by prime factorization method and lcm by grid method

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Least Common Multiple

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Least Common Multiple : 2

## What is LCM?

• Least Common Multiple(LCM)
• Least common multiple of any group of numbers is defined as the smallest number that will be the multiple of all the numbers in a group.

A multiple of a number is obtained by multiplying the number with any other number (which is an integer, whole number or 0) for eg, 5, 10, 15, 20 , 25 ,30 are multiples of 5.

• What Methods are there to find LCM
• Long Division Method
• Prime Factorization Method
• Grid Method
• Box Method
• Listing Multiples Method

## How to find the least common factor of 2 or more numbers?

LCM By Listing Multiples Method

• Step 1: List few multiples of each numbers separately.
• Step 2: Collect the first common multiple of two numbers.
• Step 3: First and smallest common multiple of two number is the LCM of the numbers.

### LCM by division method

• Step 1: Write the numbers in a line separated by comma.
• Step 2: start to divide the number by prime numbers and write the quotient in the next line.
• step 3: Repeat the process of dividing numbers by prime numbers untill you get 1 in the last row.
• Step 4: LCM of the two numbers will be the product of all prime numbers used in the long division.

Examples: LCM of 12 and 24

• Step 1: List the few multiples of 12 and 24. Multiples of 12 is 12 , 24 ,36,...
Multiples of 24 is 24 , 48 , 72,...
• Step 2: First common multiple of 12 and 24 is 24.
• Step 3: So the Least Common Multiple is 24.

### LCM by Long Division method (LCM example of 12, 24, 45)

• Step 1: Write the 12 ,24 and 45 numbers in the same line.
• Step 2: Divide all the number by 3 write the quotient 4 , 8 ,15 in the next line.Repeat the process now divide the numbers by 2, since 15 is not divisible by 2 take down 15 to next line as it is.
So we will get 2 , 4 , 15 in the next line.
Again divide the numbers by 2 we get 1 , 2 , 15 and next divide by 2 we get 1 , 1, 15.Now divide by 3 to make 15 to become 1. So in the next line 1, 1, 5 now divide the whole by 5 now the result will be 1, 1, 1.
• Step 3: Now multiply all prime numbers in the Long division method 2 x 2 x 2 x 3 x 3 x 5 = 360. So the LCM of 12 , 24 and 45 is 360.
• Long division Flow

### LCM by Prime Factorization method

• Step 1: Write down the prime factorization of each number
• Step 2: Now take the common factors and take the remaining factor and multiply the factors.
• Step 3: Multiplication of the factors will be the lcm of the numbers.
• Example: LCM of 12 and 24 using Prime factorization method.
• Prime factorization of 12 = 2 x 2 x 3,
Prime factorization of 24 = 2 x 2 x 2 x 3
we have 2 , 2 and 3 as common factor take these factors and we have one more 2 which is not a common factor take this too.
Multiply 2 x 2 x 3 x 2 this will be the lcm of 12 and 24.

### LCM By Cake Method / LCM By Ladder Method

• Step 1: This method is the one of the easiest way to find the lcm of the numbers. Write down the number in the first layer.(layer looks like top of the cake |__|.)
• Step 2: Divide the Layer numbers by prime numbers and write the result in the next Layer.If any number in the layer is not divisible then take it down as it is.
• Step 3: Continue dividing the cake layers untill you get only prime numbers in the last layer.
LCM is the product of the numbers in the left side of the layers and the last layer.
• Example: LCM of 15 and 27

### LCM By Grid Method

• Step 1: Write down the number separated by vertical line and horizontal line to separate each grid.
• Step 2: Divide the numbers by prime number and write the result in the next row grid.If any number in the upper grid is not divisible then take it down as it is.
• Step 3: Continue dividing the numbers untill you get only prime numbers in the last layer.
Product of the prime numbers will be the LCM of the numbers.
• Example: LCM of 32 and 48

### LCM By Box Method

• Step 1: Write down the number separated by vertical line and horizontal line.
• Step 2: Divide the numbers by prime number and write the result in the next line.If any number is not divisible then take it down as it is.
• Step 3: Continue dividing the numbers untill you get only prime numbers.
Product of the prime numbers will be the LCM of the numbers.

## Lowest Common Multiple (LCM) Table

What is the LCM of LCM is
8 and 12 24
6 and 8 24
6 and 9 18
9 and 12 36
4 and 6 12
8 and 10 40
6 and 10 30
9 and 15 45
4 and 10 20
12 and 18 36
12 and 15 60
3 and 5 15
3 and 8 24
3 and 4 12
4 and 8 8
7 and 8 56
5 and 6 30
7 and 9 63
10 and 12 60
8 and 9 72
6 and 7 42
3 and 7 21
4 and 7 28
12 and 16 48
4 and 5 20
5 and 7 35
6 and 12 12
3 and 9 9
4 and 9 36
6 and 15 30
5 and 7 35
4 and 5 20
10 and 15 30
15 and 20 60
16 and 24 48
2 and 3 6
18 and 24 72
5 and 10 10
3 and 6 6
4 and 12 12
12 and 20 60
2 and 5 10
2 and 6 6
24 and 36 72
15 and 25 75
5 and 8 40
14 and 21 42
12 and 30 60
5 and 9 45
6 and 14 42
12 and 5 60
7 and 12 84
2 and 4 4
16 and 20 80
5 and 15 15
8 and 14 56
8 and 20 40
4 and 14 28
2 and 7 14
18 and 27 54
15 and 18 90
2 and 9 18
20 and 30 60
24 and 30 120
18 and 30 90
3,4 and 5 60
2 and 8 8
8 and 5 40
12 and 14 84
7 and 14 98
6 and 18 18
3 and 12 12
4 and 16 16
10 and 14 70
3 and 10 30
5 and 11 55
11 and 12 132
24 and 32 96
5 and 20 20
10 and 25 50
2,3 and 5 30
7 and 11 77
6 and 16 48
8 and 15 120
9 and 10 90
9 and 24 72
2 and 12 12
36 and 48 144
30 and 45 90
8 and 16 16
24 and 40 120
30 and 40 120
8 and 18 72
15 and 35 105
16 and 18 144
2 and 10 10
21 and 28 84
7 and 21 21
18 and 20 180
4 and 18 36
7 and 10 70
12 and 24 24
20 and 25 100
4,5 and 6 60
12 and 28 84
9 and 18 18
14 and 35 70
9 and 11 99
15 and 4 60
12 and 21 84
8 and 11 88
6 and 24 24
6 and 9 18
18 and 45 90
40 and 50 200
10 and 20 20
25 and 30 150
15 and 30 30
27 and 45 135
12 and 36 36
8 and 24 24
32 and 48 96
25 and 35 175
6 and 20 60
28 and 42 84
18 and 36 36
9 and 16 144
14 and 16 112
3 and 15 15
30 and 50 150
18 and 21 126
14 and 18 126
10 and 18 90
2,3 and 7 42
14 and 24 168
12 and 40 120
3 and 6 6
1 and 5 5
4,5 and 6 60
45 and 60 180
15 and 24 120
20 and 50 100
50 and 75 150
3,4 and 5 60
30 and 42 210
7 and 14 98
3,5 and 7 105
4 and 20 20
7 and 13 91
5,6 and 7 210
8 and 32 32
8 and 28 56
30 and 36 180
2,3 and 4 12
6,8 and 12 24
8,10 and 12 120
25 and 40 200
4,6 and 8 24
32 and 40 180
16 and 40 80
21 and 35 105
14 and 28 28
9 and 27 27
12 and 13 156
2 and 8 8
5 and 6 30
12 and 16 48

## Frequently Asked Questions on LCM.

• Least common multiple of any group of numbers is defined as the smallest number that will be the multiple of all the numbers in a group.

• GCF is Greater Common Factor and LCM is Least Common Multiple.

• Commutative Property : LCM(a,b) = LCM(b,a)

• Associative Property : LCM(a , LCM(b,c)) = LCM(LCM(a,b),c)