Least Common Multiple of 11 and 12

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 11 and 12 by Prime method
• Least Common Multiple of 11 and 12 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 11 and 12. First we will calculate the prime factors of 11 and 12.

Prime Factorization of 11

Prime factors of 11 are 11. Prime factorization of 11 in exponential form is:

11 = 11¹

Prime Factorization of 12

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 2²×3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 11 and 12.

LCM(11,12) = 2²×3¹×11¹
LCM(11,12) = 132

Factors of 11

List of positive integer factors of 11 that divides 11 without a remainder.

1, 11

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 11 and 12, than apply into the LCM equation.

GCF(11,12) = 1
LCM(11,12) = ( 11 × 12) / 1
LCM(11,12) = 132 / 1
LCM(11,12) = 132

(i) The LCM of 12 and 11 is associative

LCM of 11 and 12 = LCM of 12 and 11

1. What is the LCM of 11 and 12?

Answer: LCM of 11 and 12 is 132.

2. What are the Factors of 11?

Answer: Factors of 11 are 1, 11. There are 2 integers that are factors of 11. The greatest factor of 11 is 11.

3. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

4. How to Find the LCM of 11 and 12?

Answer:

Least Common Multiple of 11 and 12 = 132

Step 1: Find the prime factorization of 11

11 = 11

Step 2: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 132 = 2 x 2 x 3 x 11

Step 4: Therefore, the least common multiple of 11 and 12 is 132.