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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Number 1

Number 2

Number 3

Find LCM

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
Cake Method (Ladder 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-long-division

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-prime

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