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 : 6

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
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