Least Common Multiple of 12 and 13

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

• Least Common Multiple of 12 and 13 by Prime method
• Least Common Multiple of 12 and 13 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 13. First we will calculate the prime factors of 12 and 13.

Prime Factorization of 12

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

12 = 2²×3¹

Prime Factorization of 13

Prime factors of 13 are 13. Prime factorization of 13 in exponential form is:

13 = 13¹

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 13.

LCM(12,13) = 2²×3¹×13¹
LCM(12,13) = 156

Factors of 12

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

1, 2, 3, 4, 6, 12

Factors of 13

List of positive integer factors of 13 that divides 13 without a remainder.

1, 13

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 13, than apply into the LCM equation.

GCF(12,13) = 1
LCM(12,13) = ( 12 × 13) / 1
LCM(12,13) = 156 / 1
LCM(12,13) = 156

(i) The LCM of 13 and 12 is associative

LCM of 12 and 13 = LCM of 13 and 12

1. What is the LCM of 12 and 13?

Answer: LCM of 12 and 13 is 156.

2. 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.

3. What are the Factors of 13?

Answer: Factors of 13 are 1, 13. There are 2 integers that are factors of 13. The greatest factor of 13 is 13.

4. How to Find the LCM of 12 and 13?

Answer:

Least Common Multiple of 12 and 13 = 156

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 13

13 = 13

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

LCM = 156 = 2 x 2 x 3 x 13

Step 4: Therefore, the least common multiple of 12 and 13 is 156.