# What is the Least Common Multiple of 5 and 13?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 5 and 13 is 65.

LCM(5,13) = 65

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## Least Common Multiple of 5 and 13 with GCF Formula

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

## Least Common Multiple (LCM) of 5 and 13 with Primes

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