Least Common Multiple of 5 and 13

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

• Least Common Multiple of 5 and 13 by Prime method
• Least Common Multiple of 5 and 13 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 13. First we will calculate the prime factors of 5 and 13.

Prime Factorization of 5

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

5 = 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 5 and 13.

LCM(5,13) = 5¹×13¹
LCM(5,13) = 65

Factors of 5

List of positive integer factors of 5 that divides 5 without a remainder.

1, 5

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 5 and 13, than apply into the LCM equation.

GCF(5,13) = 1
LCM(5,13) = ( 5 × 13) / 1
LCM(5,13) = 65 / 1
LCM(5,13) = 65

(i) The LCM of 13 and 5 is associative

LCM of 5 and 13 = LCM of 13 and 5

1. What is the LCM of 5 and 13?

Answer: LCM of 5 and 13 is 65.

2. What are the Factors of 5?

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

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 5 and 13?

Answer:

Least Common Multiple of 5 and 13 = 65

Step 1: Find the prime factorization of 5

5 = 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 = 65 = 5 x 13

Step 4: Therefore, the least common multiple of 5 and 13 is 65.