What is the Least Common Multiple of 13104 and 13116?

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 of 13104 and 13116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13104 and 13116, than apply into the LCM equation.

GCF(13104,13116) = 12
LCM(13104,13116) = ( 13104 × 13116) / 12
LCM(13104,13116) = 171872064 / 12
LCM(13104,13116) = 14322672

Least Common Multiple (LCM) of 13104 and 13116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13104 and 13116. First we will calculate the prime factors of 13104 and 13116.

Prime Factorization of 13104

Prime Factorization of 13116

Now multiplying the highest exponent prime factors to calculate the LCM of 13104 and 13116.

LCM(13104,13116) = 2⁴ × 3² × 7¹ × 13¹ × 1093¹
LCM(13104,13116) = 14322672