What is the Least Common Multiple of 23184 and 23196?

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 23184 and 23196 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23184 and 23196, than apply into the LCM equation.

GCF(23184,23196) = 12
LCM(23184,23196) = ( 23184 × 23196) / 12
LCM(23184,23196) = 537776064 / 12
LCM(23184,23196) = 44814672

Least Common Multiple (LCM) of 23184 and 23196 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23184 and 23196. First we will calculate the prime factors of 23184 and 23196.

Prime Factorization of 23184

Prime Factorization of 23196

Now multiplying the highest exponent prime factors to calculate the LCM of 23184 and 23196.

LCM(23184,23196) = 2⁴ × 3² × 7¹ × 23¹ × 1933¹
LCM(23184,23196) = 44814672