Least Common Multiple of 13 and 21

Free LCM Calculator determines the least common multiple (LCM) between 13 and 21 the smallest integer that is 273 that is divisible by both numbers.

Least Common Multiple (LCM) of 13 and 21 is 273.

LCM(13,21) = 273

LCM of 13 and 21

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

LCM of:
and

Least Common Multiple (LCM) of 13 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13 and 21. First we will calculate the prime factors of 13 and 21.

Prime Factorization of 13


13 13
1

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

13 = 131

Prime Factorization of 21


3 21
7 7
1

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 31×71

Now multiplying the highest exponent prime factors to calculate the LCM of 13 and 21.

LCM(13,21) = 31×71×131
LCM(13,21) = 273

Factors of 13

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

1, 13

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

Least Common Multiple of 13 and 21 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13 and 21, than apply into the LCM equation.

GCF(13,21) = 1
LCM(13,21) = ( 13 × 21) / 1
LCM(13,21) = 273 / 1
LCM(13,21) = 273

Properties of LCM 13 and 21

(i) The LCM of 21 and 13 is associative

LCM of 13 and 21 = LCM of 21 and 13

Frequently Asked Questions on LCM of 13 and 21

1. What is the LCM of 13 and 21?

Answer: LCM of 13 and 21 is 273.

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 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the LCM of 13 and 21?

Answer:

Least Common Multiple of 13 and 21 = 273

Step 1: Find the prime factorization of 13

13 = 13

Step 2: Find the prime factorization of 21

21 = 3 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 = 273 = 3 x 7 x 13

Step 4: Therefore, the least common multiple of 13 and 21 is 273.