left-arrow-icon
lcm-icon

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

HomeMath

Least Common Multiple


You can input in any of the fields and get equivalent values.
=
=

Least Common Multiple : 6


What is LCM?

Lcm icon
  • 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?

  • 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

Lcm icon
  • 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)

Lcm icon
  • 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

Lcm icon
  • 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-cake

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-grid

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.

Table of LCM

Conversion Table Icon

lcm of two numbers

Least Common Multiple

lcm of 8 and 12

24

lcm of 6 and 8

24

lcm of 6 and 9

18

lcm of 9 and 12

36

lcm of 4 and 6

12

lcm of 8 and 10

40

lcm of 6 and 10

30

lcm of 9 and 15

45

lcm of 4 and 10

20

lcm of 12 and 18

36

lcm of 12 and 15

60

lcm of 3 and 5

15

lcm of 3 and 8

24

lcm of 3 and 4

12

lcm of 4 and 8

8

lcm of 7 and 8

56

lcm of 5 and 6

30

lcm of 7 and 9

63

lcm of 10 and 12

60

lcm of 8 and 9

72

lcm of 6 and 7

42

lcm of 3 and 7

21

lcm of 4 and 7

28

lcm of 12 and 16

48

lcm of 4 and 5

20

lcm of 5 and 7

35

lcm of 6 and 12

12

lcm of 3 and 9

9

lcm of 4 and 9

36

lcm of 6 and 15

30

lcm of 5 and 7

35

lcm of 4 and 5

20

lcm of 10 and 15

30

lcm of 15 and 20

60

lcm of 16 and 24

48

lcm of 2 and 3

6

lcm of 18 and 24

72

lcm of 5 and 10

10

lcm of 3 and 6

6

lcm of 4 and 12

12

lcm of 12 and 20

60

lcm of 2 and 5

10

lcm of 2 and 6

6

lcm of 24 and 36

72

lcm of 15 and 25

75

lcm of 5 and 8

40

lcm of 14 and 21

42

lcm of 12 and 30

60

lcm of 5 and 9

45

lcm of 6 and 14

42

lcm of 12 and 5

60

lcm of 7 and 12

84

lcm of 2 and 4

4

lcm of 16 and 20

80

lcm of 5 and 15

15

lcm of 8 and 14

56

lcm of 8 and 20

40

lcm of 4 and 14

28

lcm of 2 and 7

14

lcm of 18 and 27

54

lcm of 15 and 18

90

lcm of 2 and 9

18

lcm of 20 and 30

60

lcm of 24 and 30

120

lcm of 18 and 30

90

lcm of 3,4 and 5

60

lcm of 2 and 8

8

lcm of 8 and 5

40

lcm of 12 and 14

84

lcm of 7 and 14

98

lcm of 6 and 18

18

lcm of 3 and 12

12

lcm of 4 and 16

16

lcm of 10 and 14

70

lcm of 3 and 10

30

lcm of 5 and 11

55

lcm of 11 and 12

132

lcm of 24 and 32

96

lcm of 5 and 20

20

lcm of 10 and 25

50

lcm of 2,3 and 5

30

lcm of 7 and 11

77

lcm of 6 and 16

48

lcm of 8 and 15

120

lcm of 9 and 10

90

lcm of 9 and 24

72

lcm of 2 and 12

12

lcm of 36 and 48

144

lcm of 30 and 45

90

lcm of 8 and 16

16

lcm of 24 and 40

120

lcm of 30 and 40

120

lcm of 8 and 18

72

lcm of 15 and 35

105

lcm of 16 and 18

144

lcm of 2 and 10

10

lcm of 21 and 28

84

lcm of 7 and 21

21

lcm of 18 and 20

180

lcm of 4 and 18

36

lcm of 7 and 10

70

lcm of 12 and 24

24

lcm of 20 and 25

100

lcm of 4,5 and 6

60

lcm of 12 and 28

84

lcm of 9 and 18

18

lcm of 14 and 35

70

lcm of 9 and 11

99

lcm of 15 and 4

60

lcm of 12 and 21

84

lcm of 8 and 11

88

lcm of 6 and 24

24

lcm of 6 and 9

18

lcm of 18 and 45

90

lcm of 40 and 50

200

lcm of 10 and 20

20

lcm of 25 and 30

150

lcm of 15 and 30

30

lcm of 27 and 45

135

lcm of 12 and 36

36

lcm of 8 and 24

24

lcm of 32 and 48

96

lcm of 25 and 35

175

lcm of 6 and 20

60

lcm of 28 and 42

84

lcm of 18 and 36

36

lcm of 9 and 16

144

lcm of 14 and 16

112

lcm of 3 and 15

15

lcm of 30 and 50

150

lcm of 18 and 21

126

lcm of 14 and 18

126

lcm of 10 and 18

90

lcm of 2,3 and 7

42

lcm of 14 and 24

168

lcm of 12 and 40

120

lcm of 3 and 6

6

lcm of 1 and 5

5

lcm of 4,5 and 6

60

lcm of 45 and 60

180

lcm of 15 and 24

120

lcm of 20 and 50

100

lcm of 50 and 75

150

lcm of 3,4 and 5

60

lcm of 30 and 42

210

lcm of 7 and 14

98

lcm of 3,5 and 7

105

lcm of 4 and 20

20

lcm of 7 and 13

91

lcm of 5,6 and 7

210

lcm of 8 and 32

32

lcm of 8 and 28

56

lcm of 30 and 36

180

lcm of 2,3 and 4

12

lcm of 6,8 and 12

24

lcm of 8,10 and 12

120

lcm of 25 and 40

200

lcm of 4,6 and 8

24

lcm of 32 and 40

180

lcm of 16 and 40

80

lcm of 21 and 35

105

lcm of 14 and 28

28

lcm of 9 and 27

27

lcm of 12 and 13

156

lcm of 2 and 8

8

lcm of 5 and 6

30

lcm of 12 and 16

48

Frequently Asked Questions on LCM.

FAQ icon

  • 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.

  • lcm is least common multiple. L for Least , C for Common and M for Multiple

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

  • LCM of 8 and 12 is 24.

  • Least common multiple of 6 and 8 is 24.

  • Least common multiple of 6 and 9 is 9

  • LCM of 9 and 12 is 72.

  • LCM of 4 and 6 is 12.

  • LCM of 8 and 10 is 40.

  • LCM of 6 and 10 is 30.

  • The smallest number that will be the multiple of all the numbers in a group.

  • Lcm of 9 and 15 is 45.

  • LCM of 12 and 18 is 36.

  • LCM of 12 and 15 is 60.

  • LCM of 3 and 5 is 15.

  • LCM of 3 and 8 is 24.

  • LCM of 8 and 12 is 24.

  • LCM of 3 and 4 is 12.

  • LCM of 4 and 8 is 8.

  • LCM of 7 and 8 is 56.

  • LCM of 5 and 6 is 30.

  • LCM of 7 and 9 is 63.

  • LCM of 10 and 12 is 60.

  • LCM of 8 and 9 is 72.

  • LCM of 6 and 7 is 42.

  • LCM of 3 and 7 is 21.

  • LCM of 4 and 7 is 28.

  • Least common multiple of 6 and 9 is 18.

  • LCM of 12 and 16 is 48.

  • Lcm of 4 and 5 is 20.

  • Lcm of 5 and 7 is 35.

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

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