Least Common Multiple of 13 and 14

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

• Least Common Multiple of 13 and 14 by Prime method
• Least Common Multiple of 13 and 14 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 13 and 14. First we will calculate the prime factors of 13 and 14.

Prime Factorization of 13

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

13 = 13¹

Prime Factorization of 14

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 2¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 13 and 14.

LCM(13,14) = 2¹×7¹×13¹
LCM(13,14) = 182

Factors of 13

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

1, 13

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13 and 14, than apply into the LCM equation.

GCF(13,14) = 1
LCM(13,14) = ( 13 × 14) / 1
LCM(13,14) = 182 / 1
LCM(13,14) = 182

(i) The LCM of 14 and 13 is associative

LCM of 13 and 14 = LCM of 14 and 13

1. What is the LCM of 13 and 14?

Answer: LCM of 13 and 14 is 182.

2. 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.

3. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

4. How to Find the LCM of 13 and 14?

Answer:

Least Common Multiple of 13 and 14 = 182

Step 1: Find the prime factorization of 13

13 = 13

Step 2: Find the prime factorization of 14

14 = 2 x 7

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

LCM = 182 = 2 x 7 x 13

Step 4: Therefore, the least common multiple of 13 and 14 is 182.