We will explore three methods to find the LCM of 15 and 12: prime factorization, listing multiples, and division method. We will also provide examples and frequently asked questions related to the LCM of 15 and 12.

What is the LCM of 15 and 12?

The LCM of two or more numbers is the smallest positive integer that is a multiple of all the numbers. In this case, we are interested in finding the LCM of 15 and 12. To do this, we need to find the smallest positive integer that is a multiple of both 15 and 12. This integer is called the LCM of 15 and 12.

LCM of 15 and 12 by Prime Factorization

One way to find the LCM of 15 and 12 is by using the prime factorization method. To use this method, we need to break down each number into its prime factors. For 15, we can write it as 3 x 5. For 12, we can write it as 2 x 2 x 3. Next, we need to identify the common prime factors and uncommon prime factors between the two numbers.

The common prime factors between 15 and 12 are 3 and 2. However, 12 has two 2’s in its prime factorization, while 15 does not have any. Therefore, we need to include both 2’s in the LCM. The LCM of 15 and 12 is then calculated by multiplying all the common factors and the remaining uncommon factors. Thus, the LCM of 15 and 12 is 2 x 2 x 3 x 5, which equals 60.

LCM of 15 and 12 by Listing Multiples

Another method to find the LCM of 15 and 12 is by listing multiples. To use this method, we need to list the multiples of each number until we find a common multiple. For 15, the multiples are 15, 30, 45, 60, 75, 90, 105, 120, etc. For 12, the multiples are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, etc.

From the lists above, we can see that the first common multiple of 15 and 12 is 60. Therefore, the LCM of 15 and 12 is 60.

LCM of 15 and 12 by Division Method

The division method is another approach to finding the LCM of two numbers. To use this method, we need to write the two numbers side by side and divide them by the smallest prime factor that divides both numbers evenly. We then repeat the process until we can no longer divide both numbers. Finally, we multiply all the prime factors and the remaining numbers to find the LCM.

For 15 and 12, the process looks like this:

Write 15 and 12 side by side: 15 | 12
Divide by the smallest prime factor, which is 3: 5 | 4
Divide by the smallest prime factor, which is 2: 5 | 2 | 2
The remaining numbers are 5 and 2. Multiply all the prime factors and the remaining numbers: 2 x 2 x 3 x 5 = 60.
Therefore, the LCM of 15 and 12 is 60.

LCM of 15 and 12 Examples

Let’s take a look at some examples to help solidify our understanding of finding the LCM of 15 and 12.

Example 1:

Find the LCM of 15 and 12.

Using the prime factorization method, we found that the LCM of 15 and 12 is 2 x 2 x 3 x 5 = 60.

Example 2:

Find the LCM of 15 and 12 using the listing multiples method.

The multiples of 15 are: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735, 750, 765, 780, 795, 810, 825, 840, 855, 870, 885, 900, 915, 930, 945, 960, 975, 990, 1005, 1020, 1035, 1050, 1065, 1080, 1095, 1110, 1125, 1140, 1155, 1170, 1185, 1200…

The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600, 612, 624, 636, 648, 660, 672, 684, 696, 708, 720, 732, 744, 756, 768, 780, 792, 804, 816, 828, 840, 852, 864, 876, 888, 900, 912, 924, 936, 948, 960…

From the lists above, we can see that the first common multiple of 15 and 12 is 60. Therefore, the LCM of 15 and 12 is 60.

LCM of 10 and 12

The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 10 and 12, you can list out the multiples of each number and look for the smallest one that they have in common.

A more efficient method is to use the formula for the LCM, which is:

LCM(a,b) = (a x b) / GCD(a,b)

Where GCD is the greatest common divisor of a and b.

In this case, GCD of 10 and 12 is 2

so, LCM(10,12) = (10 x 12) / 2 = 60

Hence, LCM of 10 and 12 is 60

LCM of 10 and 12 though Listing Multiples

The method of listing multiples to find the LCM of two numbers involves listing out the multiples of each number and looking for the smallest one that they have in common.

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, …

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, …

As we can see the smallest common multiple of 10 and 12 is 60, which is the LCM of 10 and 12.

Hence, LCM of 10 and 12 by Listing Multiples method is 60.

LCM of 10 and 12 by Prime Factorization

The prime factorization method for finding the LCM of two numbers involves breaking down each number into its prime factors, then multiplying the highest powers of each prime factor together.

To find the prime factorization of 10, we can start by dividing it by the smallest prime number, 2.
10 / 2 = 5

5 is a prime number, so the prime factorization of 10 is 2 * 5

To find the prime factorization of 12, we can start by dividing it by the smallest prime number, 2.
12 / 2 = 6

6 is not a prime number, it can be further divided by 2 to get 3.

so the prime factorization of 12 is 2^2 * 3

To find the LCM, we take the highest powers of each prime factor and multiply them together.

LCM(10, 12) = (2^2) * (3^1) * (5^1)

= 4 * 3 * 5

= 60

Hence, LCM of 10 and 12 by Prime Factorization method is 60.

LCM of 10 and 12 by Division Method

The division method for finding the LCM of two numbers involves dividing the product of the two numbers by their greatest common divisor (GCD).

The steps to find the LCM of two numbers using the division method are:

Multiply the two numbers together, in this case 10 x 12 = 120
Find the GCD of the two numbers, in this case GCD(10,12) = 2
Divide the product of the two numbers by the GCD.
LCM = (10 x 12) / GCD(10,12) = 120/2 = 60

Hence, LCM of 10 and 12 by Division Method is 60

The LCM of 7 and 12 is the smallest number among all frequent multiples of 7 and 12. The first few multiples of 7 and 12 are (7, 14, 21, 28,…) and (12, 24, 36, 48, 60, 72, 84,…).

Three common approaches—listing multiples, the division technique, and prime factorization—can be used to get the LCM of 7 and 12.

LCM of 7 and 12 means

This question’s response is 84. This article illustrates the LCM of 7 and 12 using several techniques. The smallest positive number 84 that is evenly divided by both 7 and 12 and leaves no remainder is the LCM of two non-zero integers, 7, and 12.

Common Multiple: When two or more numbers have the same numbers as their multiples, those multiples are said to be common multiples.

Least Common Multiple (LCM): The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of those numbers.

What is the LCM of 7 and 12?

LCM of 7 and 12 with Multiples

Find the least common Multiple (LCM) of 7 and 12.

Step 1: List the multiples of all the given numbers.

Multiples of 7

7 x 1 = 7
7 x 2 = 14
7 x 3 = 21
7 x 4 = 28
7 x 5 = 35
7 x 6 = 42
7 x 7 = 49
7 x 8 = 56
7 x 9 = 63
7 x 10 = 70
7 x 11 = 77
7 x 12 = 84
7 x 13 = 91

Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91…

Multiples of 12

12 x 1 = 12
12 x 2 = 24
12 x 3 = 36
12 x 4 = 48
12 x 5 = 60
12 x 6 = 72
12 x 7 = 84
12 x 8 = 96
12 x 9 = 108

Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108…

Step 2: Identify the common multiples of all the given numbers.

Common multiples of 7 and 12 are 84…

Step 3: Write the least common multiple (LCM) of all the given numbers.

Least Common Multiple (LCM) = 84 (the smallest number of the common multiples)

LCM of 7 and 12 by Division Method

   2| 7  12
  --|---------
   2| 7  6
  --|---------
   3| 7  3
  --|---------
   7| 7  1
  --|---------
    | 1  1

Least Common Multiple (LCM) = 2 x 2 x 3 x 7
LCM = 84

LCM of 7 and 12 by Prime Factorisation Method

Step 1: Find the prime factorization of 7

   7| 7
  --|---- 
    | 1

prime factorization of 7 = 7

Step 2: Find the prime factorization of 12

   2| 12
  --|----- 
   2| 6
  --|-----
   3| 3
  --|------
    | 1

prime factorization of 12 = 2 x 2 x 3

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM

7 = 7

12 = 2 x 2 x 3

LCM = 2 x 2 x 3 x 7
LCM = 84

Hence, the LCM of 7 and 12 by prime factorization is 84.

Least Common Multiple (LCM): The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of those numbers.

What is the LCM of 9 and 12?

LCM of 9 and 12 with Multiples

Find the least common Multiple (LCM) of 9 and 12.

Step 1: List the multiples of all the given numbers.

Multiples of 9

9 x 1 = 9
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
9 x 5 = 45
9 x 6 = 54

Multiples of 9 are 9, 18, 27, 36, 45, 54…

Multiples of 12

12 x 1 = 12
12 x 2 = 24
12 x 3 = 36
12 x 4 = 48
12 x 5 = 60
12 x 6 = 72

Multiples of 12 are 12, 24, 36, 48, 60, 72…

Step 2: Identify the common multiples of all the given numbers.

Common multiples of 9 and 12 are 36…

Step 3: Write the least common multiple (LCM) of all the given numbers.

Least Common Multiple (LCM) = 36 (the smallest number of the common multiples)

LCM of 9 and 12 by Division Method

   2| 9  12
  --|---------
   2| 9  6
  --|---------
   3| 9  3
  --|---------
   3| 3  1
  --|---------
     | 1  1

Least Common Multiple (LCM) = 2 x 2 x 3 x 3
LCM = 36

LCM of 9 and 12 by Prime Factorisation Method

Step 1: Find the prime factorization of 9

   3| 9
  --|---- 
   3| 3
  --|----
     | 1

prime factorization of 9 = 3 x 3

Step 2: Find the prime factorization of 12

   2| 12
  --|----- 
   2| 6
  --|-----
   3| 3
  --|------
     | 1

prime factorization of 12 = 2 x 2 x 3

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM

9 = 3 x 3

12 = 2 x 2 x 3

LCM = 2 x 2 x 3 x 3
LCM = 36

Hence, the LCM of 9 and 12 by prime factorization is 36.

Least Common Multiple (LCM): The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of those numbers.

What is the LCM of 6 and 8?

LCM of 6 and 8 by Multiples Method

Find the least common Multiple (LCM) of 6 and 8.

Step 1: List the multiples of all the given numbers.

Multiples of 6

6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30
6 x 6 = 36

Multiples of 6 are 6, 12, 18, 24, 30, 36…

Multiples of 8

8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
8 x 6 = 48

Multiples of 8 are 8, 16, 24, 32, 40, 48…

Step 2: Identify the common multipes of all the given numbers.

Common multiples of 6 and 8 are 24…

Step 3: Write the least common multiple (LCM) of all the given numbers.

Least Common Multiple (LCM) = 20 (the smallest number of the common multiples)

LCM of 6 and 8 by Division Method

   2 | 6  8
   --|---------
   2 | 3  4
   --|---------
   2 | 3  2
   --|---------
   3 | 3  1
   --|---------
      | 1  1

Least Common Multiple (LCM) = 2 x 2 x 2 x 3
LCM = 24

LCM of 6 and 8 by Prime Factorisation Method

Step 1: Find the prime factorization of 6

  2 | 6
  --|---- 
  3 | 3
  --|----
     | 1

prime factorization of 6 = 2 x 3

Step 2: Find the prime factorization of 8

   2 | 8
   --|----- 
   2 | 4
   --|-----
   2 | 2
   --|------
      | 1

prime factorization of 8 = 2 x 2 x 2

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM

6 = 2 x 3

8 = 2 x 2 x 2

LCM = 2 x 2 x 2 x 3
LCM = 24

Hence, the LCM of 6 and 8 by prime factorization is 24.

Least Common Multiple (LCM): The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of those numbers.

What is the LCM of 4 and 12?

LCM of 4 and 12 by Multiples Method

Find the least common Multiple (LCM) of 4 and 10.

Step 1: List the multiples of all the given numbers.

Multiples of 4

4 x 1 = 4
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24

Multiples of 4 are 4, 8, 12, 16, 20, 24…

Multiples of 10

12 x 1 = 12
12 x 2 = 24
12 x 3 = 36
12 x 4 = 48
12 x 5 = 60
12 x 6 = 72

Multiples of 12 are 12, 24, 36, 48, 60, 72…

Step 2: Identify the common multipes of all the given numbers.

Common multiples of 4 and 12 are 12…

Step 3: Write the least common multiple (LCM) of all the given numbers.

Least Common Multiple (LCM) = 12 (the smallest number of the common multiples)

LCM of 4 and 12 by Division Method

    2 | 4  12
    --|---------
    2 | 2   6
    --|---------
    3 | 1   3
    --|---------
       | 1   1

Least Common Multiple (LCM) = 2 x 2 x 3
LCM = 12

LCM of 4 and 12 by Prime Factorisation Method

Step 1: Find the prime factorization of 4

  2 | 4
  --|---- 
  2 | 2
  --|----
     | 1

prime factorization of 4 = 2 x 2

Step 2: Find the prime factorization of 10

  2 | 12
  --|----- 
  2 |  6
  --|-----
  3 |  3
  --|-----
     |  1

prime factorization of 12 = 2 x 2 x 3

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM

4 = 2 x 2

10 = 2 x 2 x 3

LCM = 2 x 2 x 3
LCM = 12

Hence, the LCM of 4 and 12 by prime factorization is 12.

Least Common Multiple (LCM): The Least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of those numbers.

What is the LCM of 4 and 10?

LCM of 4 and 10 by Multiples Method

Find the least common Multiple (LCM) of 4 and 10.

Step 1: List the multiples of all the given numbers.

Multiples of 4

4 x 1 = 4
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24

Multiples of 4 are 4, 8, 12, 16, 20, 24…

Multiples of 10

10 x 1 = 10
10 x 2 = 20
10 x 3 = 30
10 x 4 = 40
10 x 5 = 50
10 x 6 = 60

Multiples of 10 are 10, 20, 30, 40, 50, 60…

Step 2: Identify the common multiples of all the given numbers.

Common multiples of 4 and 10 are 20…

Step 3: Write the least common multiple (LCM) of all the given numbers.

Least Common Multiple (LCM) = 20 (the smallest number of the common multiples)

LCM of 4 and 10 by Division Method

   2 | 4,  10
   --|---------
   2 | 2,   5
   --|---------
   5 | 1,   5
   --|---------
      | 1,   1

Least Common Multiple (LCM) = 2 x 2 x 5
LCM = 20

LCM of 4 and 10 by Prime Factorisation Method

Step 1: Find the prime factorization of 4

  2 | 4
  --|---- 
  2 | 2
  --|----
     | 1

prime factorization of 4 = 2 x 2

Step 2: Find the prime factorization of 10

  2 | 10
  --|----- 
  5 |  5
  --|-----
     |  1

prime factorization of 10 = 2 x 5

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM

4 = 2 x 2

10 = 2 x 5

LCM = 2 x 2 x 5
LCM = 20

Hence, the LCM of 4 and 10 by prime factorization is 20.

Least Common Multiple (LCM): The Least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of those numbers.

What is the LCM of 8 and 12?

LCM of 8 and 12 by Multiples Method

Find the least common Multiple (LCM) of 8 and 12.

Step 1: List the multiples of all the given numbers.

Multiples of 8

8 x 1 = 8 
8 x 2 = 16 
8 x 3 = 24 
8 x 4 = 32 
8 x 5 = 40 
8 x 6 = 48 

Multiples of 8 are 8, 16, 24, 32, 40, 48...

Multiples of 12

12 x 1 = 12 
12 x 2 = 24 
12 x 3 = 36 
12 x 4 = 48 
12 x 5 = 60 
12 x 6 = 72 

Multiples of 12 are 12, 24, 36, 48, 60, 72...

Step 2: Identify the common multipes of all the given numbers.

Common multiples of 8 and 12 are 24, 48…

Step 3: Write the least common multiple (LCM) of all the given numbers.

Least Common Multiple (LCM) = 24 (the smallest number of the common multiples)

LCM of 8 and 12 by Division Method

  2 | 8,  12
  --|---------
  2 | 4   6
  --|---------
  2 | 2   3
  --|---------
  3 | 1   3
  --|---------
     | 1   1

Least Common Multiple (LCM) = 2 x 2 x 2 x 3
LCM = 24

LCM of 8 and 12 by Prime Factorisation Method

Step 1: Find the prime factorization of 8 

  2 | 8
  --|---- 
  2 | 4
  --|----
  2 | 2
  --|----
     | 1

prime factorization of 8 = 2 x 2 x 2 

Step 2: Find the prime factorization of 12


  2 | 12
  --|----- 
  2 |  6
  --|-----
  3 |  3
  --|----
     |  1

prime factorization of 12 = 2 x 2 x 3

Multiply each fator the greater number of times it occurs in steps 1 or 2 above to find the LCM

LCM = 2 x 2 x 2 x 3
LCM = 24

Hence, the LCM of 8 and 12 by prime factorization is 24.