The least common multiple or lowest common multiple of 8 and 12 is equal to 24.

**LCM(8;12) = 24**

For finding the lcm of two whole numbers we can use maths method of the decomposition into product of prime factors, of the two numbers, after the decomposition, we choose the prime factors of the two integers, and we can multiply the chosen factors for finding the lcm (least common multiple).

Example:

1) Decomposition into prime factors of 8 and 12:

8=2*2*2=2^3

12=2*2*3=2^2*3

2) Choice of prime factors :

here is the rule for selecting prime factors to calculate the lcm: when two common factors of the two integers have not the same exponent, we choose the factor with the highest exponent (between 2^3 and 2^2 we choose 2^3); when two common factors of the two integers have the same exponent, we choose one of the two factors(between 3 and 3 we choose 3); when a factor is not common we also choose it (not common prime factors do not exist between factors of 8 and 12).

The lcm of 8 and 12 is then 2^3 * 3 = 24.

The lcm of some couples of integers

### LCM of 12 and 18:

**The lcm of 12 and 18 is 36 **

### LCM of 12 and 16:

**The lcm of 12 and 16 is 48 **

### LCM of 12 and 20:

**The lcm of 12 and 20 is 60 **

### LCM of 12 and 24:

**The lcm of 12 and 24 is 24 **

### LCM of 12 and 15:

**The lcm of 12 and 15 is 60 **

### LCM of 12 and 30:

**The lcm of 12 and 30 is 60 **

### LCM of 12 and 36:

**The lcm of 12 and 36 is 36 **

### LCM of 8 and 20:

**The lcm of 8 and 20 is 40 **

### LCM of 8 and 10:

**The lcm of 8 and 10 is 40 **

### LCM of 8 and 24:

**The lcm of 8 and 24 is 24 **

### LCM of 8 and 16:

**The lcm of 8 and 16 is 16 **

### LCM of 8 and 6:

**The lcm of 8 and 6 is 24 **

**Multiples of 12**

For finding the lcm of two whole numbers we can use maths method of the decomposition into product of prime factors, of the two numbers, after the decomposition, we choose the prime factors of the two integers, and we can multiply the chosen factors for finding the lcm (least common multiple).

Example:

1) Decomposition into prime factors of 8 and 12:

8=2*2*2=2^3

12=2*2*3=2^2*3

2) Choice of prime factors :

here is the rule for selecting prime factors to calculate the lcm: when two common factors of the two integers have not the same exponent, we choose the factor with the highest exponent (between 2^3 and 2^2 we choose 2^3); when two common factors of the two integers have the same exponent, we choose one of the two factors(between 3 and 3 we choose 3); when a factor is not common we also choose it (not common prime factors do not exist between factors of 8 and 12).

The lcm of 8 and 12 is then 2^3 * 3 = 24.

The lcm of some couples of integers