Least Common Multiple of 13 and 15

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

• Least Common Multiple of 13 and 15 by Prime method
• Least Common Multiple of 13 and 15 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 13 and 15. First we will calculate the prime factors of 13 and 15.

Prime Factorization of 13

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

13 = 13¹

Prime Factorization of 15

Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:

15 = 3¹×5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 13 and 15.

LCM(13,15) = 3¹×5¹×13¹
LCM(13,15) = 195

Factors of 13

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

1, 13

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5, 15

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13 and 15, than apply into the LCM equation.

GCF(13,15) = 1
LCM(13,15) = ( 13 × 15) / 1
LCM(13,15) = 195 / 1
LCM(13,15) = 195

(i) The LCM of 15 and 13 is associative

LCM of 13 and 15 = LCM of 15 and 13

1. What is the LCM of 13 and 15?

Answer: LCM of 13 and 15 is 195.

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 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

4. How to Find the LCM of 13 and 15?

Answer:

Least Common Multiple of 13 and 15 = 195

Step 1: Find the prime factorization of 13

13 = 13

Step 2: Find the prime factorization of 15

15 = 3 x 5

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

LCM = 195 = 3 x 5 x 13

Step 4: Therefore, the least common multiple of 13 and 15 is 195.