What is the Least Common Multiple of 6 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 6 and 13 is 78.
LCM(6,13) = 78
Least Common Multiple of 6 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 6 and 13, than apply into the LCM equation.
GCF(6,13) = 1
LCM(6,13) = ( 6 × 13) / 1
LCM(6,13) = 78 / 1
LCM(6,13) = 78
Least Common Multiple (LCM) of 6 and 13 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 13. First we will calculate the prime factors of 6 and 13.
Prime Factorization of 6
Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:
6 = 21 × 31
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 6 and 13.
LCM(6,13) = 21 × 31 × 131
LCM(6,13) = 78