Least Common Multiple of 10 and 13

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

• Least Common Multiple of 10 and 13 by Prime method
• Least Common Multiple of 10 and 13 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 13. First we will calculate the prime factors of 10 and 13.

Prime Factorization of 10

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 2¹×5¹

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 10 and 13.

LCM(10,13) = 2¹×5¹×13¹
LCM(10,13) = 130

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

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 10 and 13, than apply into the LCM equation.

GCF(10,13) = 1
LCM(10,13) = ( 10 × 13) / 1
LCM(10,13) = 130 / 1
LCM(10,13) = 130

(i) The LCM of 13 and 10 is associative

LCM of 10 and 13 = LCM of 13 and 10

1. What is the LCM of 10 and 13?

Answer: LCM of 10 and 13 is 130.

2. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

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 10 and 13?

Answer:

Least Common Multiple of 10 and 13 = 130

Step 1: Find the prime factorization of 10

10 = 2 x 5

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 = 130 = 2 x 5 x 13

Step 4: Therefore, the least common multiple of 10 and 13 is 130.